{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns;sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Motivating GMM:Weakness of K-Means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "x,y_true=make_blobs(n_samples=400,centers=4,cluster_std=0.60,\n",
    "                   random_state=0)\n",
    "x=x[:,::-1] # flip axes for better plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2201bea3710>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans=KMeans(4,random_state=0)\n",
    "labels=kmeans.fit(x).predict(x)\n",
    "plt.scatter(x[:,0],x[:,1],c=labels,s=40,cmap='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The k-means model has no intrinsic measure of\n",
    "probability or uncertainty of cluster assignments**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "from scipy.spatial.distance import cdist\n",
    "\n",
    "def plot_kmeans(kmeans,x,n_clusters=4,rseed=0,ax=None):\n",
    "    labels=kmeans.fit_predict(x)\n",
    "    \n",
    "    ax=plt.gca()\n",
    "    ax.axis('equal')\n",
    "    ax.scatter(x[:,0],x[:,1],c=labels,s=40,cmap='viridis',zorder=2)\n",
    "    \n",
    "    centers=kmeans.cluster_centers_\n",
    "    radii=[cdist(x[labels==i],[center]).max() \n",
    "           for i,center in enumerate(centers)]\n",
    "    for c,r in zip(centers,radii):\n",
    "        ax.add_patch(plt.Circle(c,r,fc='#CCCCCC',lw=3,alpha=0.5,zorder=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kmeans=KMeans(n_clusters=4,random_state=0)\n",
    "plot_kmeans(kmeans,x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**for k-means cluster models must be circular；\n",
    "k-means  cannot tackle oblong or elliptical clusters**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng=np.random.RandomState(13)\n",
    "x_streched=np.dot(x,rng.randn(2,2))\n",
    "\n",
    "kmeans=KMeans(n_clusters=4,random_state=0)\n",
    "plot_kmeans(kmeans,x_streched)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generalizing E–M: Gaussian Mixture Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2201c812898>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.mixture import GMM\n",
    "gmm=GMM(n_components=4).fit(x)\n",
    "labels=gmm.predict(x)\n",
    "plt.scatter(x[:,0],x[:,1],c=labels,s=40,cmap='viridis')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "### The predict_proba method returns a matrix of size [n_samples, n_clusters] \n",
    "### which measures the probability that any point belongs to the given cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.52 0.   0.48 0.  ]\n",
      " [0.   0.   0.   1.  ]\n",
      " [0.   0.   0.   1.  ]\n",
      " [1.   0.   0.   0.  ]\n",
      " [0.   0.   0.   1.  ]]\n"
     ]
    }
   ],
   "source": [
    "probs=gmm.predict_proba(x)\n",
    "print(probs[:5].round(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Visualize this uncertainty by making the size of each point \n",
    "### proportional to the certainty of its prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2201c6fd7b8>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "size=50*probs.max(1)**2 # square emphasizes differences\n",
    "plt.scatter(x[:,0],x[:,1],c=labels,s=size,cmap='viridis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## visualize the locations and shapes of the GMM clusters by drawing ellipses based on the GMM output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position,covariance,ax=None,**kwargs):\n",
    "    ax=plt.gca()\n",
    "    \n",
    "    if covariance.shape==(2,2):\n",
    "        U,s,Vt=np.linalg.svd(covariance)\n",
    "        angle=np.degrees(np.arctan2(U[1,0],U[0,0]))\n",
    "        width,height=2*np.sqrt(s)\n",
    "    else:\n",
    "        angle=0\n",
    "        width,height=2*np.sqrt(covariance)\n",
    "        \n",
    "    for nsig in range(1,4):\n",
    "        ax.add_patch(Ellipse(position,nsig*width,nsig*height,\n",
    "                             angle,**kwargs))\n",
    "        \n",
    "def plot_gmm(gmm,x,label=True,ax=None):\n",
    "    ax=plt.gca()\n",
    "    labels=gmm.fit(x).predict(x)\n",
    "    if label:\n",
    "        ax.scatter(x[:,0],x[:,1],c=labels,s=40,cmap='viridis',zorder=2)\n",
    "    else:\n",
    "        ax.scatter(x[:,0],x[:,1],s=40,zorder=2)\n",
    "        \n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor=0.2/gmm.weights_.max()\n",
    "    for pos,covar,w in zip(gmm.means_,gmm.covars_,gmm.weights_):\n",
    "        draw_ellipse(pos,covar,alpha=w*w_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dJkPEDUbNhBHvaFzNS2mzp7/1BNv//MaAaePk1npaj7RgcWc3U7QfPAUZxFuUJc5FvbUTmw4MCPcZGt48xLGNB5h13UJmXb+IzuOt6FlMSI1vHmbbM9u5dl36nEfLhRBvRdXwBmKEJoxoa5Ra/4LTtA8dCW9sNd74dSMepaPjC8UIhOO47GYKnGZEw5fcIEcmzO1+LMUPhuLv8nHgxd0M1YMTbx6kcEpJ1uNm37IkY7sSS5A0dIwNMcMGlmiSMvty6wy4CC55YDVXf/w2ymdPgSwmjdaDp8btGgcQjSlpewPnkkA4Tmt3iGA0MUGEG6Y6/40q539TZH2dYusr1Li/SYXtVzkfr+lJEW/tDo3b+8ng8mHCiHc+vtTHdx4n4ksXRiWSQFM0ijNk6iusLqFmxey09vpX9vD0P/xiXCtvTUm/IUkmGZsns5eLvfCsi+Di+1fz4A8+gaeyOGNfW4E9L++Zricr/JxrEopKW08oGemq61jEZqY4/odprm9SbnsMgdg5n8NYsEv1FFpeZ/CCWRQUim3rEYXRBU4pqkZHX5hub2TCbMgaXDguavHWNI2dL+7hpV++im8Um37ZKKytwJKh6IFklimvq+T+//gYM69biLXAgbXAzoy181n3o79Jn5eqsuP3m4j4xpmjPIMPcCIco6imNK3dU1XCwrtXprSJksj0VXPS+rorilh49wqicTUvIhDJsLmbT7zBGK3d4YGbhFPexSzP5ym3P0Gx9WWmOH/GjIIvXpQC7jLvQRLTffktUicOOT19cC4EowlaukITfoPW4Nxy0dq824638+PP/pxjO0+ADu4yN1e/73rWvHdkW2ImNE3HWlRA7Zp5HFq/M+W1qVfMZPKCaQDc9pV3jjhW98lOehraxzSPkZAsMlF/etrZ8tlTMmZIXPWRWxAlkcYtR4gFo5TUTuKKd1+LvTC5eo/EVZzW8ZeAg/xHW6qaRrc3SmSIeWeS/Y+Ypa6UNrd5L2W2p+iIjPz5nE8iSjW6LiIIqTdJRXMRVasBKDK/TIFlC6DjTyyhJ3oXI5nbNF2nyxshZlcpdFmMvCoGaVy04v3b//cHju04W4ze3+nnlZ9sYMbKOibNHH0FmTMCcf3n7sVV7qF51wnQdKYuq2XJu9ZmPS4RjeNv68VRUoAgCphsZjSzGZPdQiKcvhKsWFJL296GjKvqXCioKqNjSPg7wOldDcSCESxD/L9FSWTVR25h1UduyZgjJRJVxh20k8iTb/1gYnGVLm8EJcOTgVU+lfEYq9SY93mMF39iJYHEYtzmXSnt3thVJLRyJtt/Rrn9j4hC8qmi0LIRh3yUU8G/z238/mjRUo8NOQ9Fpw0uHS5K8Q56QxwfJNxniAai7HlhJ7d+dvTiHe63/4qSyIr33cCK990AgNNlzViCDGDrb17h0IadBNq9CJKIIIoUTy9nxi3LqVg0nVNbUh+LC6rLuPoLD7L/Dxs5un4Hanz4x157mYeiaWX0NrQhiCKlc6oJdPSlbagChHr89DZ1UTGvOut4mVZniqoRV1TM46hPqetJAc9XAiZ/OE6fP5Z1Q1LRCrBI6U82iu7Oy/nzi8AJ/1epdPys30wi4Y8vpTX8ISShj2LrhgHhBhAEnULLa3SG7yeq5ZYDPpZQae0OUeqxXVRBUwYXlovymyAk83Fmf22UaLo+6sjMwy/uYtujrw244+mqhq5qdNW34G3uZuVn70Y0y3QcaEJLKBTVVrDo3dchW0wsef+NTFpSy2v/8miaEMtWEya7lcKaSSxYdw3FMyajqRqCIHB6ez1v/PsTGefjKHFTNLVs1NcOEEto4xJvgLii5kW8e/1R/OHhg616o9dhk4+niF5MLaMrcve4z38u0HQXzcHPpbU7TfsxS71p7bIYxmXZQTSSewEPTdfp7ItQXGC9YH73BhcXF6V4OwrszLpiBrte2pvSbnPbWXrXFaMebywh9Q1vHsrqR50Ix2jZWs+qz96DGlfQVC1pTlFU6p/fRvexFvwtPRlX0KLJxNovrePIc9t4+3+eTVbhWTaTefevoWX70Yz5TgDqblyMxZm+2ZoLiqIC4/vBxxMajrGdHkgGWXX7ojltwnVGkwWaCq2vYxJ8RNSpdITXEdemjH0CF4CoMh1FcyCLqR5Oui4CCskvSO6LER2dbl8EVdMpcIwvAMtg4nNRijfA+77xMOFAlKPbj6EpGoWTC7nmAzdSWjP6wruJLII4HMoIJo94f7ZAySwjkczjvfnfH6dl29ERx93yg2fwNXUOtPUcbSERjqZU5xmMrdDJ6o/eMroLGHxOdfz+0mN5D8+g92++hXN2XRTojK6jM7oOi3iKEtuzFFlfxKo00R29g4vva6tRYHobk9RJX2wtqp6soxrTpuCLr6TY+kpKb0HQmOL4OR7zDhr8/4yqF4zqbH2BZOGQQtfEStlrkF8utl/BAGVTS/nKU19g1+uHaG7oZO51C7CMoh7lYJR+4ek81sLeJ7cQ7PLhKvOw6IFVOLPUniyfXUXTtmNZxyysmZTyd9Nbh2jZPrxwQ9JXe7Bwn6Hh9X1ZXcanXTlrXN4GiqrlXPAhG+oYxVvXdTq9kTH5nLtNW5nq+jfMUk9/ywYKzFs54f86cHHkzDaLLUxzfQun6RCCoFNhf5TOyP10RN4FQFPgiyTUEjyWzVik1gF/cFFQcZt3McXxY5qCXxz1eX2h5Ga5IeCXLxeteEPSvj3jypmUzMm+SZcLcUWj40gzz3/1MYKdvoH203sbePDfP4SjIj3QZfnD19J5tIWTGcqOlS+Yxpy7Uwst9BxryWgmGYxrchGOMg/BDHlJYsP4jHumjf5pYygJdXx2b3WM3jNdvuiYg4XK7X8YJNxJCsxbKLK8SG/s9jGNCaBpoKgqCUUnoapJxyBdB32QIUNIfv9EQcAki8iyiEkSGXr/q3L+EJf54MDfZqmHSfbf4o8vI6LOQsdES/gTyKIPq5xeuMNhOpjWliu+UAxRYMIVzTDIDxe1eAN5SWavKBq7n3grRbgB/G19bPv9Jq773L1px8hmmbv+9X00bjlCy/6T9LT0YnHZ8FSXUXvD4mRek0EMLZAwgChgspoxOaxMXjqTxo37Rj3/QLc/9XriCnq/nT1XFFVnPOmkx/I59AVihMcYaCIQxyqdTG8XwCHX5yzemgbxhIovFKM3EENRtIEnsdHPSUCSRcySgCxLWOQIdvlQWj9ZjFBoeZVIeFbK0dlGHQ99wRiyLOLIQw53g4nFmH7OdXV1JuAXwDSS0RvfqK+vfyaP8xpgrI/rZzjzQ82UMRDA3565HZIrr+mr5jB5+SyC/R4Suq5z6Km3OL2tHiUSwzO1nPkPXcPMW5dx6Kk3iQeHuB1qOolwjEQ4Rv3zW0dcnWeioDoZcRkLR9n438/StO0osWAUURbxTC5m4T0rmXvbsmELHicUFUZwM4uFY7QeOU3J1DJcxakh+rrOqNLDBsLxgUf7saAjo+puIP3zycVlMJ7QCMcSRKLJYg0KAtFxpgvQ0VEUFUUBYgqSEEMrJYsFJ9Uzpy9+NUXWVxCFVE+bQGLhuOYE0O2NIheJWMwXhynJ4Pww1rXYe4Ce+vr699bV1RUDu4FzI97jTIqk9R/vLM38g3eVjSwEinrWZW3f71/n4BNnsxL6mrvxnupi7T8+RGKETc6xCHf5whqqVs2jr6Wb9V/7Pd3H2gZe0xSV7oZ2Xv3+0zS+fYQ7/uU9WetfaiO8j6/+7EW2P7EFb1sfdo+Dudct4J4vP5SSx1zNUbwjMYVe/3hD2UW8sTVYpcdSTBVRdVJWl0FN04nEVEIxpd/D5tyi6jZ6I3OYbNqS0q5oTnqjN6W0+eNX0RZ6F6W25zFL3aiaFX9iGS3BT417Hjo6HX1hKoodRjHky4ixivefgccH/X3uUqGN12rSf/yCd6ygZU8j4b6zyYIcJW6WPbgm42E9TZ0kIjHKZ1VyRgc0VUsG5gyZk+9UJxu++HP0PGQ+PINklpl6zXyWfegWdv58A02bDxAfZiXb+NYR6l/Zy5ybM2dAHO593P/SHl796Uuo/VGoYW+IHU+9jbPIyS2fuSu3QfpJKBpd3kheMgK2hj+MjoTH/CaSGCCi1NIefhhFT80AeabCzoUoiXag/eOYpBBFtkNIokIoXkZj7310RSpx2HQk6eydpz3yAfpiV1Ns24AvdhUhZWne5pH0Aw9TUeIw0speJoxJvOvr64MAdXV1LpIi/uWRjikstCOPYcMsjjCu7HjRmEJMh9lr5iJ+ZR0bf/gCUX+Y0hkVrP7QTVTOn5rSv6epkw3ffpzTextRFZVJs6dwxQdvomxRLf62XkJZzC/xQHo+kkwIkpjqyy2QoomiWaZmzTyu+PDNOEoKOPzCdo69uDOnm1jP8Vac92euWG+3yngKzobWewrtA/9/7K2DA8I9mJM7j6f0Ky5xDVsZXdd1WrqCFBTYs/YZLVH+lnb+NpluQBQwO+GMpV/TdQKhOLF4HJPZhMk8vN3X7Upev8N0jHLbK0m/6chaAom545hhFYf6vo87eBCL3ElP9Co03YZogpgGBXYTTpsZUCkRv41dfA1Z8FNqe5WgdjO92t9xxu4tEMUlPIMo+Alpa0kwc9SzEUwypf2fWWnpyDVYLzUup2se8xZWXV1dFfAU8MP6+vrHRurf1ze2DHy9vWFi41jRRuMKwUCMxq31bPyvvwzYuEM9AVRF453/9VEig4oaP/+vf+L07oaBv9sPn+b1/3yGm7/1QTZ+608Z07jmiiBL6IOOt7jtzLl/FT1HWgh3+3GUupl1x5WU9XvXREIxmrfV5/z0IdnMWUP9EzEJqX/T0VNoxzvo84hkqTofiyRS+tlEMA8j3t5gDG/w/GT+i8VVfKF4zpuPbpcNfyDCtMJnmF38O0xyMnCmwvEcx3se4njPQ+Oaj59aoLb/r7M3cq8vjFmWmFv+J9zuvwy0y0IvBeIf8YXL6Y7eg10+zDTnd7DJTcn5Cr+lK/IOWsOfGNU8+rwhIsEYU6sK6eoafybOiURpqeuSvOZsN6QxGcjq6urKgZeAL9bX1/9iHPM65wgC6JrG1l+9krI5qakaTduO8sfP/AS9PzlST2M7rQea0sYItPaw7cfP012fueSZyZHdVcta4KBq1Ryck4tShBsg5g9z9NntaAkF0SRidtqwFw+1wef2COya5GHRkJSxuY4ybcn0jO1T5qe6aA73NB6Lq/iy3ATyiabpeAMxevzRUXuNSEKE2qKnB4QbwCRFqSl8BrOUfeN6vMQVFZu4I61dEHQKzNsBqHT8HJvp7HdPFiOU2Z/CIe8f9fl6/NFxb/QbXPyMdXfjS0Ah8JW6urrX+//LXkdsHIzXfCcIAn3NXXRmEd6T249zbOMBABLRRNaVdaQ38x1dNMvMf2ANYoYVqWw1UXvTEq7++weIZylSHO720bLjGF2Hmjn+0i7Wf+6n7PzlSxx+ZguNG/dRvmBaRuUVRAFBFJHMMpMXTuXmR9ZhLxrmkXGY9/Gqd17N4tuXIfebHQRRoGZ5Lbd89q7sBw1C05Nh2+fa3hyJKXT2jSZSM5Vy53bs5vQAKavJS4XrjfFOb1gEIdsTm4okBLDL6fEEkhDHYxn9vFRNo7MvNzOewcRlrDbvzwKfzfNcMjLezRdRALPDhmw1oWTxOW4/3Mys6xZSXldJ6YzJdB1LDaawFjooX1iTceXtnlzM7LuuQpBljj77doovuRJNcOSZtymoKu0vmTYyiXCM+me3DvxdUF1G9ao5dO5vIuoPI9tMTLuijpu/9CCy2ZRz5ORw76Moiaz71vtY8eAJTu5uoGRqGXOvX4A4pChuNk8Tfyg+rvD5XAiGEyMmtBqJcKIMVTMhiamfhaYLRBLZy+Dlg77IHIod6T7hwcQCdF1G0zP77GdrH4lQJIEJHbv1og/lMBgjF/0nK+XoV5z9eBFniZvKRTU0bc0cvu7oLy8miCKrPnwzr//3s/hak5F9Vo+d5e++jsmr5tG68xh9g4owiCaJmrULEESB2XdcScfexrRAIDWuJANzxngT8p3qxOq08tCPPsXpXScoq6ukbMbZlLi5hrxLOeSCnra0lmlLa7O+nqnCuaJq59xc4gvG81JVxhudTW94HqXOPantkdl0hq6p2/7VAAAgAElEQVQc9/iDsUqd1BY/icPSRkzxcMp7Iw7zacqcu5DEBIpqoTe6qr+4hEQgsZhi6dWUMeJqEd3RO8c8h75AFJvFYRRyuES55MVbEARkSeTGf7iPP3/mp/hbU1N0lkwvZ8EgW3Hl4hpKZ1YQ7PGjxhKYbVZEUUC2mln7jw9x4PE38J7swOSwUr1qDjXXLmLvY6/TffQ0XUfSiygAtO0Ze3EGgK6jLaDpzL9j9BkVz2CSxnsTzHy8N5A9L/d40fXkJugZbyNRiCOLIeKqh7FGJu5u/RxLJv8bRbYjIGjEFA/Hu+9lqAVxsvt1pnrWYzd1EUmU0OS9mRb/jTmdwyL1sKL6X3Bbz9qwy5w72d3yeRp676HAdpze8Fx80Trcdg2nXeJU8O8QUHCbdyIJYcLKDNrDD5PQxp4aIaFqBCIJ3HYjA+GlyMUv3nmoHiJLAo4iN+//zefY/OP1nNpxDDWhUDpjMtd+8raB8mKJaJynPv/zgSrtAP62Xrb830vcWFlK4cxKrvzEHWdfa+3hqY/8J7EMRY1TyCLcgixmTTub0k8UECWReDhG0/ajFFQUUTarMvvpVJUjL++hu6GDUK8fQRAoLHFxxX1XUTl7bGlVpQziH0uoBM9hncWzwq0yt+znTHK9jVnyk1AdKJoNRbfji8zkSNd7ULTcXMRs5nacllYkKTlvu7mH+ZN+SvR0Cb5YMpy9zLGdheU/GtjYtJs7cVsbUTQbHcHVOM1NlDl3EIpPpiO4gqHCP73o6RThBrDKXmqKnmX76X+mN7JgoN0fjoMg4LQ5aQz8C7LQiyT6iKnV5CP5ljcQw2k15RwZazBxuOjFOx8BB7IsQVxFEEWu+dQdKa81vXWIbd/4ExF/iHBvMD28naQd+ugL24hFE/Q1tCNbzVQsnk77gZMjC3cGzE4bc+9bzeSlM1j/+Z9mzeF9hskLpnLijUPsfvwNgp0+JLPMlMXTufmRB7EVOFL6xkJRnvvyb2nZm14y7MBLe7jnyw+x5sHMvuDDkenH3xc4d26B3sDZFffs0t9QW3w2gNcknf2MimxHcVma2HLqm+Sy/15T+Dw2U2qyK7u5m2lFz7G3LVlQYUrBKykeKclzRqjyvEKpY3/ydSmCpgv0heeys+WLxNSiQeNlrm9qN2Vu94diCIDDJqPoRSiDxhovmq7jC8WN7IOXIBd9LK1JHr94ZzIZ6LrOs1/6FX/58qO0HWjCe6o7o3CfoXnncU5vrSfU5cPX3MWRZ7fibewY03xshU7m3nMVBVUllAyzghYkkYoF05h7+3Le/uXLA/Z0Na7QtO0oG3/wXNox2377akbhBgj1BXnj0dfRx5BywDTkCSiWUPsLE+efYERJ8Sgpc+4cpjcU2w/m7C1ik7tGbDdL/ox9nObTTC18HpOU9OQQBZ1ix0HmlP0ypV9USc9SOVw7JDMExhPnJqQ/EI6PmB7BYOJx0a+8TbKU9NUex3cvU76Hv373cRrfHjn/9hmGE/bRUjwzKdiCILDoPdez7UfP4z/dDYDZZWP2XSsprCnH4XFQu3Q6m/73eRKR9E3B1gMn0VQ1JSHVUE+ZoXQ1dBDLUDh5JIYG5wRC52aTMqFoaWPL4vABXoKg47I005ZDfEZEKc18Xs3JvLKfYpb8SGL2z1oU0r+IhbZUN7/G3rsod27HYT57c0+oNk55bx52bt5AnBKPjQz7wuNC03WC4QRuo/rOJcVFL96QFN94YuyuaJIoIonCQE7qRDTO0ddyDH4QBUpqyuk+kfmRdyQEWUzmiVY1EAXK5lazpL/4MUDZnGpu/beP0PDaXhLhGFPXzMNZ5gHA47YiCAK6nuXaNT3tpjZSmlhHoQOz1Uw0Prqb0eAboKJqhKL5X3XrOvQF42kboP7odBwZ/LPPoOkS3kjSXi0KMWQxnHVTs7H3HZQ7tmKSz16/rkOJfRdm+exNTVUlJGlQDc2EG190Oi5L+s1R01N/RuFEJTtOP5L0NjG1EVM9nPLeTEdweHOVomn4QrFzYuLwh+OGeF9iTAjxNsvSuMQbwGaRCfaHwR95eXfGXB5DESSBK95zPeV1lTz3lUfTbNPOiiI0TSOcId+JZDUx+86VTLtmPpqi0ranAXdlMZXLZ6a5bskWE7NuXZ46tt2M3G9nnr56Hgef35E250lzq1Oy/gHUXj2Ppu3H0LI8gs+9YWHWzIPDYR4k3oFw4px4mARC8YzZAOu7H8ZpacFlSW4k63qq52VHYDldoUUsKP8fylzbsEpeNF0mrhbQHljB4a4PAskYsrjqSnPbFARShBtIEW4AkxwgoTpRNDOymPpk0BOenzZnf2wGu1u/kPO1nyESU7CYpLz7ZyuqRjiqGH7flxAT4pM0m8TB6SLGhM16VrxHsvla3Hbc5R7m3LKUxfetQtd1Zl67gKOvnC2IbHbZWPDQNVStnM1r33iMroOnUsZQowna9zcw7/7VyBYThaOohmOzylgH5WauXlrL0nVXs/+ZrUR9YRAEJs+vZs0nbkPXNGLBKGaHBVGSmHvLMsK9QY68tAtvSw+SSUY2SRRWFjP32vlc97HR18I0yeLADUfXdQLjDJbJRCye3XMlEJvO5pPfY5rnBcyyD3QFm7kHSUjQF6njRM/9zC3/OdOKNgwcIxJHlrqYXvwcFtnH8cBXASh3bRuwWY8GUdBxWto42vUuphWux27uJKHY6Y3OJKYWMKXgZVp816Hn4SflD8WxmKSMHj7jIRCOG+J9CTEhPsnhMtnliiyKmE0S8YRKzcrZbBSfG8hpMoAA7/75ZyiYXIxkkgcESxAEbnnkQaqXzaR1XyMmm5lZNy7GNLmUeDBCoC29rBlAT30LR9fvYO49uXt3WK1yxqooV33wJubfeQUnNh/CPamQmqtmc/jFnez7y1a8LT04ilzMWDuflR+4keXvWsuSB1YT8YaomlaC1Tq+x+XB7380ruZ980vTGDHQR9XsnOh9INsIlDl2ZT22zLGL5nAb4CEcL0fXBYQMtuuRkMQIJ3of5KT3Doqsh5js3kSFewvlzuRNvabwOXa1/D2hRNWoxx6Mput4gzGKC6zjGmco0biKqmkZg60MJh4T4lM0m6RxB+sAA6uOo6/sTRdukuYLm8eJbDalmTYEUWTurUu58v03IFtMHHphO6df20O0N0A0S94TAH9Ld87zcznMODMIdyISR1VUXKUeFt+3iumr5tC86wSb/vd5OutbiAej9J3qYvujr7P7T0mvC8kkUzi5aNzCDWCznBXvfEQ6DiUYSaAMfB46AqPzuhDQkMXsq2mTHMIun0bTdBq7l9EZqEvrk8v9KBq3EI0nUFQ7gqhSWbAxZRXvsZ1gTtmvRzX3bMQSKtFYfr1PdHTC52CvwuDCMCFW3gBWi0QoMr4vntUkIQgC8WjmVZ6maFnzn0CyYPFL3/4zwY6zIfBVS2uxFNizFhA25VDxXpYlnHbTgI178Pm2//Y1uo63YXZYqF4+k2v+5k5ks8yRv+5OL86g65x46xBL110NgH2Esme5Yh1U/DKSb0HR6a9zqVNX8muqPS9hEsMkNAcNvXdxovedI4+BjC86Hasps0thKF5Gi29mf3UfndeOfZYrqh+l1HUUXZcIxwqo8KQnhhpqW5/k3s/iiv/kzYa/ZW7ZDiQx/b0ocexDFkIouiPttdESjiawWvJb2iwcU3AZEZeXBBNi5Q35ESJBELBZJGZcMz+jqJbVVeIq92Q9fucfNqUIN0DzrhPDVn73nc7sVwzJJ4oCpwWP05wm3BFfiL9+9wmad50g6g/jb+vjwLPb2PiDZwFIZLE7x0NnvSiseahpaDVLAwE60biCmuGJZTxEYgqarjOz+A/MLHkcq8mPJClYTT7mlD1KTeGTOY1ztPthgrHJae2KauZI+00EwmZARxLizJu0Hpelk0i8iJM9V9EZnJU+IOnpaEQBakrepNy1j2g880/HJIVZWf1PWKTejK+PhmhCJZFDBO6oxoypeSnqbXDhmTDibR1P6fNBOG0mSmsrWPLA6hQBL5hcxMoP3jhsEp+eMQTldB8+TajTiySLyLKE1SrjcpgpdFtxO8xZaw7u+8tW/Bls6U3bj6LEEpTOTBcqgNLaCgBcdjOiIODv8rHlj5upf+PQmIJzrINumufikfuMy2G1Z0OaWAoCTC/6S4aj0vFG69h88j841PFe2gPL6Aou5Hj3Dbxy9O/Z13LPQL9rZv4XCyqfocx9jHJ3PYumPEWlZ2/GDAaZ3i5ZVKgo2M+JrrVEE5lX14X248ws+UNO8x6JfJupdPQxp9Q1uLiYMGYTURSwWqRx2wElUcTtMLPyAzcyc+0Cmt4+TMvBUyQicbb95jWath1l5ftvzOgvbXXb07IGjoQSjSOGwhQ6K0Z13OAVdEp7MEI8EmPpg2to2dtI887jA68VT5/EFe+7HlkWcVhl/vqj9bz9pzcI9QYRJIFpS2pZ9833ppQ2G4nBTzzRPNbohKSHSaLfNdAkZX56scg+kqWERt7zUDQHJ3rXcaI3mUJ2aARoqbOeKZ7daccVO04RjBXjsqaGzWfb2IzEPfSGa9jR9F5W1PwCk5T+FOS2nBxxvrkQiaq47bkVfs6VaFzBaRu+ZJzBxc+EEW8Al82Ul00ch9VEOKZQXFPO8Vf30LjlyECpsdZ9jfQ0dHD3dz6QtgqvXT2X7hNtoyqK7JlSQsW86pE7DqFycQ17nnwrzbe8eHoFtoJkms+7v/1+Dr+0m56GdhxFLhbcsxKzzUKBw8yJ7cfY9MtXSPTnEddVncYdx3nhe0/zyZ/lVrHcapYGngw0Xc/7I/zgVWVUKczowicKCrNLf8WRrg/2t+hMcr3JFPcrKJqDht678cfO1nr0WI9Q4dqALPjxRqawv+VuFC15syp2NCBL6StZQThjXrmRqsIdiIJKVHHhtral9e0NVXOsKxlkdazrBqYU7mBacXqVnIQ2fpt38mqTm4xOe/7ENjbOmAmDi4MJJd42i4woCnmx2XkcZlpavBx6eU+aGDfvOk7DW4epXZ1amPbK912Pruuc2HyQqD+MaJIJtGd2EwQwO60sfmDVQIWa0VCzcjazb1zEkZf3oPdfr6PEzfKH1w7cVERJYt5tqcE9dquMWZY4+Nd9A8I9mKY9ycLKueAYtDqLJ/JbmV1V9ZSV/MH2j3Fl1dcQxVRhEQSY7N7Mse53oepWVlR9mVLH3gETS6V7M4e63kdT3zuY5HiTeZN+htV05uloGxXuA7x4+J8BK23+eaialHGjURIUtjR+nC2NH6fYcZzb5n4VSUy93kjCycZjn8Fja2Z+xXO4bG2g6yiqjCydXeWrmpk2/5q8vE+QNC3lU7wVRUPTdaPK/ARnQom3IAg4rDKB8PjtgCZZItrlJZDBDKJrOj0N7WniLQgCKz9wIys/cCOaqtH49hFe+H+/GxDXM5TMrGDKounMvnFxWurWWDCKbJGRTMO/9YIgcOMXHmD6qrmc3tOAyW5hwV1X4irLvqEqCgKufnOPkOUxWxCFnJLzCwIpAR35Xq3FhkSAdoWXc9p3DdWFr6f1tZm6sMh9OC0nU4QbQBRV5pT+humFz2GVexGHCHO5+yhzJz1Pg+9hfJFq+sJVlDhPpp3DFzv7OU0t2oZJTs//YhLjWOQAV8/4IS7r2Y3ohGrCHynDLIcJx0toCdzIaX9ydS4JUWaVPkaB5RiabqYjeCVN3tsZTT5yVdNIKFrW/ZHRoqMTT6h520cyuDBMuE/PaTPlRbwBps6ejLvcg39IeLsgiVk3BM8gSiINmw+lCTckhXdo6tmTW+vZ8fuN9DR2YHHamLZiFld/6o608HaAcG+Ahi1HKJpaSu3V86i9el5O11PgNA/YRhfcvJgdT7+dltBq6pLpOYXHO6ymlJVZvjPexTOs/juDK6jybEyzM4fjk4kqJSyc9F8ZCxJJoordnN2rp8DWCv336A2H/pm7F/5Din07FCvgYOvZijUJLbN7Z0K1UFu6KUW4AUxSgo5oBZuPfwqbyYtCFRYLgMbyKd+gbFDlnlLnbmymbo50vT/rfDOeO4/iDcmbcR5CAAwuIBNOvM0mKS8blwA2p40V963krz95MUWEp14xk2kr0gM5hqIkMu/aD81B4u/o45XvPUWoO5lqNBaIsO/ptxFEgbWfTi3yu+UXL3Pg+e1E+oKIJokpi6Zz65cfwuoe3obqtJlSVlI1S2u54eO3sOX3m/B1+JDNMjXLa7nzH+4d8bqAtCRG8TzbuzPlqmkLrqYzuJRy11l/bVUz0ey7AU03oWUR1ZHPZWde+W8x04k/Vs76A19j9qSXKLC1Ek24qe+8iZ7Q2fJvRztupK7sr7isqQFW7f55WOXMAVlFjgbuXPBPuKzdBKMltAbW4ovOpMSxN6WfKGhMdr/Ose6HUPXca3bHE2peQ9sT5yj9rMH5Y8KJN4DHYaE9Nnya0Fy59x/vw+JxcuD1A6hxhfI5VVz5nmtzMi1ULpzGsdf2pbWX16VWq9n/zLYB4R7Mya1HufqTGmpcoeNoC4GOXnb+cdNAUiktoXJqxzE2/2g9N30xW2h4MoApU+DF2g/eyIoHVnN40wGKq0qpXjhtxGsCcFjltFWemscCw5qmo2QcT2RHy5eYUfw4HutRVN1Cm38VrYFrATjW8xClrl0Z07Jmwx8tYUrRHgpsZzcfq4u289fDjxBVMpugYkoBWxo/ylU1P8Vp6UEQksWQCqynB9nTU7GZAghCUtid1m5mWJ6iM7gk41wd5i6umPI1DnV+BH8se83QweT75qkavt4Tngkp3hZz/lbfgiCw+p1Xs+y+q0ZdGWbBXVfSdvAUxzcdGFhtV8yfyqqPpiZ/imfJnx0PRdn2u9c4smEX/vY+BEnMWFWn9UBThqOTWMwSHkf2FanVZWPJKGtfFjhTx9N0Pa/5TIbLEKnpFo52vzvja33ReZzsvZ2phRsGNh01TUzb5NR1CMSK6Q7UIYlxpg7xBil1NrCk6vc09qymOzgTRUtfAdtN3djNPQNmGlGAIufpjPPKtAkqChpWuQ9NFzIKeKlzP0vlf2fzye/ntAJXVA1Ny5/LYOabp8FEYkKKN+R39Q3JIKBC1+hKewmiyC1feogFd13B6T2NFFQWM3PtgjSb8uT5U9n/zNtpXi12j5Ntv3l1oMblSOXQhmIxSxQ6LXmtDn6uV90wPuE42PlJGnrvY5J7MzGliFiikIUV/43TkrRDa5rIie41vHHi04DAHfMfyTjOzLKNzJ70KoFoKfUdN7G/9aw5qdKzixU1vyDXzLkxxY7dnG5Oiat2ukOLKXOm+5YDuKzNTPVsoCN4JdWeDchilN7IPFr815Apfi6haFjyEDULxsr7UmBcOyB1dXUr6urqXs/TXEaFxSylJEzKB0kBH71dNRaKEeoN0HH4NF0n0n2DZ123gFnXLUyJt3ZPKiTiC+VUVX5yBj9x6zkQbkhfdQMoar6zCI5tPIvUy5zSXzCn/JfY5D56w/PoiSxhw+HvsLv5QVq98/BGKihzHuWGuu9S5jxELJG5MPGZlbLL2sWiKY9T6TlrZ18w+S+YpNyf6kKxkoztPaEZ7Dj9TzT03oGuZ/6cCu0HWTX1H5hR8hTTitazZPL3WDL5e2QKJsin4Ob7acrg/DPmlXddXd0XgPcCo6/AmyeK3FZau0PjKpE2FKtZptQj0heMoeRgZ9z0w+fZ+/SWgSrwh17cyeqP3sqCu64c6COIIrf80zpqr5lP676TWJxWqpfP5Im/+9mwY5/ZsLz6U7entBc4LXlLOpU6buZw/Xyv0pQxfGA2UwdXTvlaSlX2Mud2dpz+Er3+CmIJJ2XuemQxab4qsLdT7jrAobbbmFRwMGMU5BlMUpxpxW/T4l2GJMbw2JpznlcsYWdb0/tZVPk0kwv2IYoami7Q6l3A3pZ1OGxWDnZ8nEJbPYW24ynHarpImWMX8qC5CYLOZPdmWvxX0xlcOaR/ztPKCVXVEfNQI9bgwjAeBTgB3Af8NpfOhYX2ZBX3PGN1WOjxja++ZKZw8ZJiB75QHP8wtRo7j7dyaP2OAeGGZK3LvU++xRUPrEIe4ke75I7lLLx5MZt+soFX/v3JYc0kskXmvu98gBmDfM3NskSxx4o8hko4Qxl6zSZZpKrMldGmag7GUIX8uanFdTCPMnBpRsHTKcIN4LK0Mrv8L3SFPsOM8i0Dwn0GiynKvMr1HO++nVLnEWymbsySP6OQm2VwOKwImEhobmxkT/OraiKSqOGLTuFY9zsIact4q3kpk71b8dga8EVqaAmsRDILuF1Je3ZbeB0O8w8GihvrOqi6JUtUqcbkgiNEhetS2p1286ieDAs9w3soFRU7Ljlf79LSzE9alyJj/uTq6+ufqKurm5Zr/76+/NmnB6PrOqFAdMyh255CO95h5mYWdLzBeMZH/UOv7EtPywr0NnXSsP04kzN4d6z/2u859vrI9TMr5k1l0sLpBAPJG5PDZsJsEgn6x18IefA1+zq8JKJx5iyqpqcnmLG/PxynLw/nPYPPFx3IaZIrZs+pzO1CM6FQFLOYOdLVLEVxmRt59cS/EQpFWFP7Q2aWvZ7SR9OhuXcOof58Mid7lrGwsiXrXIKxEjYe+xx94Wo03QQkjzsWWgws7u8VAwSs/dVw/IGr6PROosrzMrIYRUChuvDV7OeI2vAHUoVdTSig5pZUqtDjoM87/EOxVcpPoZOLhdJSF11dOVShnmBkuyFN+NuuIAgUu620956bm4PFJFNaIBGIxNOy6jlKCjIeY3ZYcJalv9ZzsoOTW9PzRg/FU1XKyg/eBIDJJOGyyVhGiMgcLd72Pp7++p9o2HkcNaFQu7iGh/7xPuZdPSe9c54f18cyXEzN5taXbPdFKnHbMmd99NibOZPcakfTu3FZOihzH0EUdOKKlcbu1RzvOrvK3XXqYURBYW7FC2Ry7tB1mZ5QLbIYYW7F89hMPrqCMzjZcxWp20ipVxqI13Co82MA1Bb9Oeu1huPFnOy7Pa0973VDDZP3hGbCizckNy8LnOYRS2mNFVEUKHBYcNnMhGIK4WgCTdOpu2Ehe598i86jqau0qmUzcE8qTBun82hLWsTjGQqrS/BMKWHK4unMv+NKXAW25Gr7HJiaAJ782h849uaRgb+P7TjBz7/wG775169iHep6mGez6FiGO9V3M6X23VhMZ/3lE4qdJm8yDP1A212UuQ9hkdOfEGKKa+CsUcXD+kNfpbpoG25LO62+hfiilSye8ieKHY3EFRun+pazu/mdTCt6C6c1vbh0h382HlsT1878TwodSfdBTYfpJW/w2tHPow9Uk89+pa3+q6ktfhLLkKCfhGpjZ8sXULT01ZZwMXwQBhcNl4R4A3iclnNSOmowoijgsplwWmWiCZVgJMEt//QQb/70RTqOnE5uMC6u4ZpP35nx+CmLp2MtsCeLCA/C7LByx9feQ1F1GQ6bCbtVRj6HdQa7mjpp3Hkirb29oYNNf3iDmz98Q0p7vn/juY7nNJ9kVsnvKbA2omh2OkNLMEt+7OZOIolSmry39G/qRWn3z+fVo5/jhlnfxzxIwDUdmnrObB5r1JW9RE3JmyRUO95INaFYITfUfYdKz1lTVm3pG4TjHiIJD05SxTsY87Cr+Z2srPnFgHBD0g98atEO6spe5kjHbck2UUAUkuYTTU8Nooook2jovZfaoicwy0nzRjhewoGOj+ONZk6HYGitwWDGJd719fUngZUj9TtflBRYaesO59U7ItYfYGMZVLhBEARsZhmbWaZwQTXT/uPDRKNxEqo+rEeAq8xD3Q2L2fvUlpRM//NuWszM+dXIsnheMr1FAhGUDBkHASLB9A20fLsjipIAI5huZTHM8infwWU56/lRYD3O8Z772Xb662fHEkEURTRNpdjeTCBWjlPvRBBUgrESTvasYm/Lg5R6Orh+wdcodpwa8NisZhc1xZvT8ngLAjgsXmxmLx2BGThMfZjkML2hqexruZ+oUkiR42TGeZe6jnGk4zYc5k6uqvkNpa56dER6I3M42P5xYmrRQN/jPQ/RFriKSvcmNF1C1yQKbUmzWkdwJUPlOpecNKPByCo4sblkVt6QLLRQ6rHlxf7d19bLc999kqa9J0HXqV44jTu/cB9FlcUp/WRJRJbEAdc9vT/vdULVkkKu62dLCQgCd/zDvVTNrqRhaz2CDrUrZ7HyoTV5F8jhmDK3iqq5VTQfTHWJcxY6uOreFWn981H8eTByDtc6zfNcinBDUlQrXG9xsu8OokopZ8RNlgTmVz7GgsqnU2zUibCDfa33A7C08keUONM3PYcK92BEAXRN5sm9/4UsRokp7oFzJtTMUZHJdp21M39AufusWarS9CZmMcjbzf+a0j8Ur6LZdwPLK7+Jx9YAJItA9EVm8lbTt9E5u2LP88eAJBniPZG5pMQbkvbvEo+Vbu/YvSN0XefPX/4djTvO+uUefv0AEV+Yj/3yM8MKrSAImE0S5mF28VevW8PqdfnL9zxanDYz6x65j18/8ihdzUnxshfYufNvbqOsujStfz5cEweTywrSLKfbmgHs5jaum/5JAvFqTvTcS1vgGixygpqSt9LErdx9jOXVv6HUeZwy17ExzdUkh1E1C+qQpFinvUspdjSmZDmMJJwc77yWKZ6dlLrSN6aL7Afx2A7jjaRuCteVPDog3JD09S6yH+X66R9j6+mvEoxPA/J7ExUFwVh5T3AuOfGGZDpT1aWPOlfJGRq2H6Npd0Nae9O+Ro6+dYS61Rk8MiYIZpNIebED002LmL1iJq8+upF4JMGqe1cwaXp5xmPyvUIbWmw5E77ojLTq7ZBcfYpSjELbMeZP+jHBWBUW0YbdnLng78zS17CYxn4j7wtPy9i+u/khJCFOddE2rCY//shkDrbdQXdoJnXlGzLmM5FEBbvcgZfU74/Hlr7/AGC3dDO//P94u/kbAHlNCZvvpymD888lKd6QTGmq6b+SZkkAACAASURBVPqYPFC8bX1oGQJodFXH1zb+quAXClkWKSu0Dfxw7W47d37qthGPO7NKG0s4tU06RontWUyil6hSRXvknZhNIwdStPjXMtm9mUmu7Vn7WGU/VZ6XOdz5IYLRin6XwLPoOuMS7t5QFXtO35/SJqCyoPJpKtwHEASNpp4VHGq/jUiimDMmlZM9K1ky5Qls5tSnh1C8lI7QlQxFGSbVrcd2BIvUh0pxXutY5vtpyuD8c0l/gh6nhQLn6DPOz7t+IQXl6X7F7jIP829anOGIix9ZFikvtCGN0YtFGsOP3WnawYyCRyizPUuhZTMVjseY6f4CshTMQTwkdpz+EgfaP8pp7zUkVGvGXrIYRUemyXsTCTX1sw5Ey7KOrusQV6wklPT1i6KK7D19D88f+FcC0dSiHCun/4xl1X9gsucAFQWHWDjlGVbW/JLBm4sxpZDGvnekzDmh2GnovQdVS4/m7QwuT2s7O08RHRFzHlfdYKy8LwUu2ZX3GTxOC5Io0OvP3YRiddm4+v3X89cfvkA0mFy5WZxWVr9nLfaC/BSWPZ9YzRKlHtu4Vm5mWRx1VGS57XHMUuqGoNN8hHLbn+k1PTxidkEdE419dwNwhfh1Jrm3pr6uQ294LjZTBx7bacLxImQxQjThoal3BZ3BmdxY952U+pJnEARSXApTzytxum9ZWqrYqYVvMqNkc1r/KZ7dlDkP0xlMmkNsFokTvQ/RE15EhXsz6AIt/mvxx2pxmJqpK30Mt/UEqmanI7ico93rsMrdVHleSTO39EXmElcLsNvy6+9vuoQiKy9XLnnxBnDZzUiiSLcvknMSq9XvXkvN8hnsfWEHOrD41qVMnlN1Tud5LnBYZYoLrOP2ZrGYpJRq77lglTLnv7ZILZhliXC/v6BF6qGm6Bksso9grIqTfXeg6qkr7fruh3FYWnBZzgTFiLT519AWXMnqqY9QYG0c6Gsz+5DEGGY5TFPPMqaXbs1YPi0bJinB9NJNdAZnAyAIyv/P3psHx5Gm552/LzPrPlCFmwABEuABnt1ks+9junume3p6Znouj257LK21HilWsau1Y23ZuxurXe+GV7GxG3uErbHDkixf0kgazYykkWb6vptHk02ySZAgQeIibhRQ95HH9+0fhatQVTiLlwdPRAcbWVlfZlVlPvl97/u8z8tn9v6/dEZPY1RwGzR0i8bQDabSB9ENHf984+Z4vod4fqkjky7yPLzzdwh7Bxe31Xn7MbQ8Fyd+k3h+P3vr/5SAZxpH6szlDvLp5LcBaj7z9rj+s150/1Tgp4K8odhMt0X3Mz2XW7cOvK2nnbae9rV3rCHmxmd5/w/fYmZ4imBDmMe++SSdD3ZtaqxwYGNGRqvBvYmb3ZL1eCn3CLFkkJbgR0grAkhOtP8OQc+SlW5L8BSnRn4bRy2FGJKFPbw3+H+xO/I3uPU4sdwRptKPsrf+T0uIG4pJzYh/goj/r8gWNmdU5NIWVmqKYzu/S3fjR1X3NW0Pk8keoFjEVe050Rn5mxLihuIKoDX0EVenv8Vs9jAz3uuYzk1ydhNXpn6ZnLUDQ9MwakjeArGqGmob9wd+asgbirPH1gY/sWT+tlZibhbJ6QR/+Bv/isn+icVt1z68ys/+r7/EvicOrHscTSv6vdSy56HbpSMQG/LXiOVfJODqQxNLSWPLCRH1fEir/4fsqXNhOQG8rtLEXkOgl+6G73N9RUcdR/q5MVuaQPS6SvtMroTfk9qUZfBE6gDtdZ/w4M4/o2kNmeHI3CPEMvsI+l0YuqIr+oP5BgyS2dxB+md+FoULr6tystujx6n3f8oDrf+CgHsKgCg3CHmGOTPyP6K71tcqbb1w3aFisG3cXvxUkTcUs+wtUT/JjLlpKeHtwvv//q0S4gZIzyT56I/eXTd5ez06DeHa2MYuhyYELkOr2PW9GmKFVwCNeu/rGCKOJesJuK7g0Ypdb3TNQtcq67kbfRcZMV4kb1dPOgJkzLZVX4fi7Ha57FDKYmVmNUgp8BmzHGv/HsFVinjyVoBLY1/h0thXCfrdeN06R1p+l93RHy0eqzl4nrBnmLOj/4R4tgdZX94WLW12sLPuzUXiXkDIM0Z3ww+ZNv/Rmp9xI9jMKmob9x5+6sh7AeFA8WaT+r2zfJwdqUwUsVvVCWQBQhSTsyu7vtcSXre+IfIGiBW+RKzwJQDa/N+hznNuXe9rDF7m2a7fIG21MzT7MqPJ51GUe4APxb/IjtD7NASuVhhlCULAWOIgE4mj3Jo7zs7oeXaELxH0TRDylH6/mqboaX2doKfyg2UBqXwLqXwrwYAXj0vHrcdoC79XFl9vDp4m6utlPP0kk+nH2BE6ufiaaQe5OftldkV/XPEYIc8EMbu2s+T/3Dy8f1rxU/0rul06jY1BrLxZ1bP7TiJcwUYWoK7K9gUEvAaRkOe2a3f9XoNkdvPOjUJUJv5KxTgAbiNLvXGd+vbr7Gn4Ppcmvk0sVyrVlMrN6Vv/E/sa/oyW0EkCrjE0rfLvOJk8zIXRnwEglt3LhdFv8mT3v6Sn5a3yY1dokrDyfJtCN3l2///NSPwyFyf+axr9F/AYybL9Dc0i4utjLneIs7d+i13Rvybqu4rt+LmV+Cxz+UO0hk5XPJakvOJ1KxCI29KFaRt3Hj/16ychBCG/m/bGACH/xrq71BpP/PwzRNvrS7Z5Al5OfL2y95fbpdFa76cx4rsjRRdet7FpnTjAXOFZHFmu104VOpnL7auq5QYIe0c41PL7QPkDwJYhrkz/Cm/f/FdcGP9NMoXyUIvleHHpOfwrYuSJ3M6Kx0vlG7BlOclZjqvkQaMJRXvdW7SF3mBvw/cqjmVLF/FcUXWiMBic+wqfjP0jPp38DebyxU5JQ/EvULDCJe/L2/XMFL5ScczNwuvRa1rss427B/23f/u378iBslnzzhxogwgEPGSzZtEp0GMQ8BYJfLOdebZ0LtEgu491k88UMNwG7Qd38sKvv8wDnz9esp/HrVMf8lC/ydj2wmfeDGxbbjh0sgBLNgMSnz6ArhVQSpCxDtI7/T9wZeob+F3jJR4fK+GZbzqctXZU3SdZ6GZw7kvoWha3nkQTBYSQ6JpNc+g6XY0nSRbaSeaKY7iNFN2NH5TN/BO5dkbjx4n6h9G04rWQLjTgNdIVSvYlLcGTeF2JiiuIqfRxbsz+7KrfTdbaQcZspt5/BU2YKKWTszpJmM9hq3Jv+LXg87rJV5B21gXcVbvnCDmLR/0ZhurDoRvE3Z3MbBRbua7vZQQCnv+50vbt9dMKuAyN+rCXSNBDKmuSylo1b8C7GtoPd/ILv/N3K77m9xqEV7n57gT8XoNUlYYS68FE7lvM5F8m6nkXSzYRN59Gc2kYWo7pzEPzhSrVHpwCtY7FosKgd+rvM5U+waMd/6yEUAPuGMd3fp+k+RiWrdhdf74i4QY8s7x27X9jNPk0OyOf4Kggk6lneLrrH1YMjaz2DB2crezvvhIdkTfxLVOk1HmvYOj/nKvx3wW2/psLRFUFkkf+OT71HXSK8X+f+k9kxH+HpT215eOuF0opHFn8T8ql/1dKlSiGhCiumHWtaNug68X/v9thzzuNbfKuAk0T1M0nAHMFh2zBIpu3a9qpfj3wuHX8HqPYoOEe8KPwunV0TcORm1+Z2KqJ6fyS5E/Tip3rx5NPMzR3iZ11b+DSy6sf47m9xLJH132cxsBFdK28urLOO0DQk6RgRKtWGvpcCb569B9QsOsZSXyOseRzQLGUvSNSvffkSmTMJmarNFdYjoDrFg3+ixW2XyfqfoM58/PrPmY1LPx2KyHkHD71rxeJG0BnBJ/6F1jqcRC1nyxYtsSyHSxbYs7/Z29xtZu1FalkDpdLx21ouAxt/t97R5RQS2yT9xoQojhb8XsNVFiRNx2yeZu85Wz5YqsETRN4XBpej4Hfc28Q9nIUcwQu4unayiw9bp2g182lyV9neO4ldtf/BY2BTwi4YyglSOT3cGny22wsTVP597Ec/2Lp+3jqKToir2NopasJl16gTh8Choj6riBQjCaf5+LEb6BrBVpDH6zpry2lznD8pYp+Jivhdc3i0it/py69NmZoIX9lJZKbv0Znumy7QR+6uoAjHtrysW1Hkjcd8qZN3nRwnNszC7Idhe3YLE8365rA69bxegy8bv2eu6c2i23y3gAW4uK++Wy9lIqC5WBaDgVb4jgSx1HrCrMIUTR7MnSBS9dwu3Q8Lr2mtp+3C0Gfi0TarHlD3FDATcGWJM1uLk78JgKbpuBZlDSYzh5no/l1n6tyQ+Kc3bRYfh/LPsj1mZ9jd/RH+FyzSFWuw3bpeXbWvc5o8nmkcpPId9MW/mDN489mD9Af+/l1netc7iCpQjshT2lFqi1DxAvPrGuM1eDStVWKtqolio1VXlsbli3J5C1yBRvTuvM5pAU4UpHJ22TmG4gbRrF5StBn3Nez8m3y3gI0rZTMF7A8dlfCb6JYuq3r93eFm6FrBLwG6fmEmFLFB5mcj03qIk1r4Ae4tWlyTgdT2a+gaZ41VQ5CQDToZjqeR6FQGEylyzv7rBdh70jF7TmrseTv/tjPMTT3Ms2hM3SEX6cp+GnZe4KeEaK+XuZyB8veXw15e337AUjlYnDumxxo+n1cerEpsaPcTOW+iim3btEQWkX/XxBfwqv+IwZDJdstjuKIjXnXS6nIFmzSOYuCee9VMUMx6Z60TZIZE7dLI+B1EfBtTUl1N7BN3rcBQggMXXAfP9QrwrKdYnzSkuRNm5l4HqlUyRLY5xrnkZ3/jLB3iQjCxjucufXbOCow35RXoOkCQ9NwGwJD1zGM+ZZmhkY44CaR2XpYppIsEShzCwSwZJjRxOcIu4crkrffNcsTnf+U2exhzo/9JnO5/UR916oeWyqNqcyJDZ1vWr5CX/whGrx/gxA28cJnyNjrj/FXgyYEQd8qyhHhJSP+MQH1/6FzFTCweICM+K3KAvwKsGxJKmuSzll3PC+0FZiWxLQKxNMF/J6iIOB+8X3ZJu9tVIRSxZBQruAshoZW3pSaJrDM0uXw/oY/LiFuKHqV7G34E65O/0oxrIQCGwo4ZJaN5dIFrvnwkd9rkM2v0aV4DUylTxD1lfqSmI6P0eRz6CKPQkeqUlLrn/0aTcFzZWZXUOyE0xS8wKGW3+Ps6D/mYNO/JeK7giEKCOGgaXkMTVKwQ9xKfI7R5PPrPte6oAe3S6cgOxnLfntzH7gKQn73mis9W3uMhHoEXV1C4UWKfasSt+NIXjt/nZHpOC2RMA/sbkfcx/3tlWIxtOLzGtT53Xjc9zaJb5P3NhaxsOTNF2xyprOm9CrsdzNtllYihjxDFfcNeQbXPHZBKgqWJI2FrglsWyGVxOXSN0UL12Z+AZeeoTV4Eq9rjlShnfHk43TX/5CI9/9A4iKWOcqlyV/DlkWfdsuJcnL4f2FPw/doDX5E0FMeN4/6e8lb9Zwb+8cl2+u8fdR5bzKVPrGmJ0vJ+wIeAjU0EVsOTQjq1muZIDQc8cCau8UzOf7n//QavSNLXiyHdrbw6y8/jcd1/1NKLm+Ty9t43TqRkOeuSnNXw6a/6Z6eHg34l8CDQAH41b6+vv7V37WNexF50yadtcgWNiaFdBla2QzZlJWbVVhOcEPn5EiFy9BIZW1SWQuPW8frNjA21E9T5/Lkt7k69S3q60xicQ9Pdf0jIt6lQiB/5C10Lc/Z0f9+6TM4Ua5M/SoCSdDzF2WjuvUkQsiy7yqR7yGxzL97PQgHPAR8y29Dm6j7TVz6HHOFZ7Fk64bGW4lIaO1cw0YgleLf/ORMCXED9N6a5G/OXeFrj209zHOvIG86TMSyhPwu6oLuey4mvpWz+Rrg7evrewL4LeD/rM0pbeNOQEpFMmMyNpNhcjZHZpMa9pC/tFx8PPkMzoqycsv2byiEUDq+G69HJ19wiKcKxNMmedPZkM7FUT4KTivtde+UEPcCmvwX8BrlUrmJ1GNUWnzowqYlWNmLZL0QCCJBD8FlxO3Vb3Ag8ut01/1zOoLf4WDk27T6/nDTx3AZOqHVYt0bRCZvMTaT4cZ4ZaO04en7t7/rakhlLcZmsqSyJuoeCuhvZY3zNPBjgL6+vpM9PT3VG/EB0agf4x7N4DU1bc6w/36EIxWxRI6so8DQCYa2/pu4PC6SmaJOOqG+xmDSotn/Oh59hpy9g/HMKxT0pwmH1xioCsJhL5mcRTq3VO5tOkVDLq/HWLdyJ+zPVNzuMrLUh7OkrdJEpqHvmo/jlt6wQkBTeJgM5YnP9UAIaKjzlamUWvXfw68tLV5depIdge+iPM9isnahz0rs72rA7906eTuOZDqewxEa4bCPgK9yGCbg9xCNrq1pv524ncdXgCU0mqP+e0LSuxXyDgOJZX87PT09Rl9fX8Us09xcdguHun1oagoxPZ2626dx2yGVIpW1SGZM6up8Nf09lFJkM+ZiT8pk8hWu8GU0Yc0nBAWw+S7uC9CVIp1bsitIpUDXi3JN7xrJpXDIx1DsITqCf4zLKP3syXwn47PtKErj92nhI9vQQsBd6rGuFMymWkimqjsPVoNh6ESCbvK5AvnckqJGFyk668tVLprIoZs/YS67e0PH6WiLkEnlyaS29r3nTZuZRL5EUXSovYVLg+MljzRD1zja0VbT60oqxcm+Qa6NTeHWDR4/sJvuloaq+0ej/jvCM5NTKRrCnpo8GNeDapPLrZB3Elg+qlaNuLdxd5HKmiTS5m3zaBFCEA25mUnkl4VeBFLV1lvc7dKJGhrpvLXYCclxFOmsRc50CHj0VWVeaXM3Q4mX6Ir+FbpWnMUX7BD9sW+gKtwKUnkYTX6GvQ1/VuK3Mps7tOEwkKBYmRrwuSqKOIrKl2q348ZuU13TaIr4mJ2tvNJYD5RSxNPm4opqOT77wH5S+QJnro8wm87QFA7y1MFuHt3XuenjVTr+H7xxilPXlhLgp/uH+OaTx3j6YHfNjrMZSKmYjucJ+hyiYc9dq9nYCnl/ALwC/ElPT8/jQPm0YRt3FZYtmU3myd+BYolifNW9Jb/v9UAIQcjnxuuSpHPW4mzfsSVJW+J2S4Jeo2qS7srU32M6fYKW0GmkdDGceIGMWb2xdN/036FgR2gJnsLQCiRye7k684uoDRhFeVw6dQHPopa9EqTyk7EewK2/W7LdciLM5L+w7mMBNNZ50bdQAi6lYjqRq9oqUAjB1x57gC+dOEwyl6fO78WocVOT3pEJPr4+XLItW7D40w8+YWd9HbtXmYHfKaRzFqbt0HSHLJlXYivk/X3gxZ6eng8prot/pTantI2tQilFMmuRSBfuaMFE0O8ib92ZUmiXoREJucnl7RKVjGk6xG2J31s9lDKTPcZM9ljF18ohGJz7CoNzG/fV1oQgHHCvu5foUPq/QYgCIdd5dK1Azu5kIvsLG6qwDPvdZbH0jcB2JFNzuXVZIrsMnYZQZXXRVnF9bBqnwsWbM22+85MP+K1vvEAkeHfj61As8pmYzdIc8d3x4p5N/8p9fX0S+LUanss2agDLlswkcnfNSyIa9DA9X3l5u1G0OHXhcelkCzaF+UIiKYuhFNNyCPpcd7z5gCaK3WqC/o0d21H13Ej+73i1QQx9lox1tGLrt2pwGUVd8mZhWg5T8dxtM43aCOoC1T1VZtM53vz0Ot944sE7eEbV4TiKybkcTRHvHW0xd/dTptuoGXIFm4nZ7F01AdJ1jWjIgxCQUTmyauuJyvUcM+R30xD2Fju4zysBTEuSyJjYd4iMvC6daMhDS72fcNC96YdGXu4mbT20IeLWhKA54tt0/LVgOUzO3RvEDfD0wT20N1Rv/zeXyW3JlrjWkFIxNZcjV7hzab/7vxxqGwAk0kUN9L2AGeb4U/t9Bu1JBIIO0cxLxuNEtdsryRRC4HMb+NwGtiPJmTamKUmkC/iq2KFuFbqm4Vuw710lpn07IRC0bEG+ZtkO03O5u9bMQKGwbYllS2xHYjsKy5F8/ZHj/P6bH5I1y6/rkMfH1FwOIYorDpcucHldmLaDS9ewHYnlOPg9t68hd9nnUDAdz9Ec9d2RGfg2ed/nkEoRS+S37ANSK0gl+Q/xNxmylyrw+tUtTPs9/o7rZcQdyswbukbI50b5FLatULL4r9etY29yxiYQGIZWJApDx2UU/73bBpFNEe+mfThsRxZn3HeYuKWS5AoOuYJdNb7eVBfkK48+wF+euUimsETgHQ1RHtu/GygSpmk5mBboqTyxuQw/OnuJm5MzmLZNR2OELz98mAM7W+7Ex5on8Dwt0dsfA98m7/sYUiom5+5umGQlLuQHGLKmyraPqClG5CSd+tbKvTcKgcBlCAI+F47lYBiChqAfx5FYTnHGJ9W8M7mat/AVgBBoFMMRhqHNk7Z214l6JaIh76b1xo6UdzRUolAUTIes6WCa66voPdjeSsDj4ZObw2RNk+a6EE/2dOM2SqnLtG2+/+F5zlwfImcuFXNdG5vmD944zUvHDzA4HQMERzp38Mjejts2kZBSMRXPbWk1tB5sk/d9io2oAu4kkk7lIgmFIs3Gi1pqjYIpSaQKRMJe3PdXf90y1AU86zedWgGlilrl29ENaiWkkqSzVrGDziZm+J2NUToaIiSyeVy6hs9d+pmVUvzxB2e5MVFucQAwl8nyx++fW/z79LVBhqZm+Zmn1qs42jgcp0jgO+r9ty1hvk3e9yEWlrp34sbbKB727eUnqY+Jy9ICkXoRYp9WXU+9AEdJHBzcyzqXK6WIqQQe4SYkti4PK1iSeDJPJOxds5XZvYpI0EMkuHllSTxt1qRZglSK8zdvMZ1Ic6izlY7GpU73CkU2X2zMsJV4+uB0jDcuXmVsNoGua+xuauDLDx8h7CvaE/SPTzEwObOBc4YPrg7w2Qf20hDamGHaRmDP11k0RjZno7AWtsn7PoMjizPue5G4AQK6jxdCx/nr5Bmyqlj+HdR8vBx6mDrlJVslG+8oh5/Yp7gpRylg0SLqeVp/EBuHd51PGFMzuDHYJVr5kvEUQW1rJH4/E3h9yEt4kzNugGzerlg5uVEkMjn+9asfcn28SJw/OtvLY/t28YvPnsC0JclllgmbhWk7/OWZT5lJpQGwpaRvbBJ5RnJsdwenrw8yEU9uWJqaLZh8eGWYF4/tv63JxUzexpM1q/YP3Qq2yfs+glTqngqVSCWxbFXsAu4Uk4IKeED1sMPTwkXnBkIIHjL200gYw6Xhkhqm5ZQZ9//YPsUnsm/x70E1zqydRKJIUwzFmNhcV7f4kf0hP+d+YcvnX7Ak8XSB+i1oo+8kBIKGOu/qXXHWgO1IYsnayDe/99GFReIGyFs27/beoCVax+GdbTU5xvmBkUXiXo6bkzOMTM+Rt1dP1C9cZSup3dAETeEgc6kCHrdN2O+qeZXoAuZSBTyu1a0bNoNt8r6PMJvI37XkpEIVW0bZTlHSZctV45cRwnxGP178QxY16Mz7MJmmQ7ZgFxOBmgAdbshbZWMkqezNMaQmSKsswVqEUAoOSc0iHFgfIYZdp2j2/QleYwRb1jObf56p/M/Cbe4iU/Qr2XoRSCyRr5kkcGCy3AJWAX23JmtG3nnLqri92CN2deJui9bx/JH9nL4+yPUV8fCulkZ2NRVL7Aumw4zlEA548G+hOrUalIKZRJ4dDf6aJkm3yfs+QSJdWOx+fSfhSEmuYJPN2zWTk3k9BoaukcyaFKQiT4G8x1w3/9nYWKwer12Ik0sUTSKy6r6ZnIWhizXL2H16P7tCv4NbnwPAo0/jM/oBjan8z6zv5DcBj0uviX9GJm/V1Oemmn9KLZsWHO5o48O+myUKEgC3YWBWmHV7DIPu1kb272jheNdOhBDsamrg1Qu9DM3MgVJ0Nkb5/IOHSt6nVPEesx1J+DaEOCxbksxam04wV8I2ed8HyOatO16AU7AcMgV73ZKujcIwNCIhD9eyY3zIeSzKZ1gC0NGxVxD1DtFIhOqJpik5y4/tk9xS0ygUbaKRr5lPE6U6iSczJoau4XZVJ55G318uEvcCNOEQ8bxz28g77HfPV6xubcYmpWIutfWmzsuxv62JsdlEyTaXrnGoY0fJtplkmvev3mA2lcHvdXOiu5N9O5baxDlS8snNEcbmEvjcLh7dt5s6fzHJ1xAK8MT+bt7rvY41r893GzodjRFuTJQnKXvaW/hbjx8v2eZxGbzy8Nrt3aD4ILelIhp017wnZyJdIOA1amZitU3e9ziKXiW3v8R8AdlCUR3gbDHRtB5Y2LypnyRGsuw1oWC/6qJRC/MxvRTmyT1KiOf041XJTCnFj+wPGVVLy+RRNc2fp9/ll/Uvo4vKN45SEE8XaKzzUW3iqIvKvu+GVn7+W4UmivHtQI08oxMZs+Z67m8++SBzqRxXxyYpWDYRv4+H9+4qIeZENscfvX+GmdRSCGxgcoavPXqMgztbcaTkj97/mOvjS7UBl4bH+Mbjx9nVVA9AV3MDp/oHsPLFCYxpO8QzOVojYSbiS999c12IR/buIpMvEPBuPo9RKNjMKVV8aNaQwJUqxr+baqQ+2SbvexyxZP6OOAPaTlEdULBuv33sAs45fRWJW1Maz5qPsF/tRiDodncw5LqFBzfH9f0lMsKVGJTjJcS9gHEnxhUxwBF9T9X3Oo4imSlUNXfK213AWxW276465mYQ9LmoD3lrpg+2bEnqNlj1ZvIO33j8OHPpDLF0lo6GaFkD4o/6bpYQNxQTm2f6hzi4s5WP+4dKiBsgns3x3pV+djU9Whzj2k0y+dLzj6UyHOls40hHG7F0Brehk8jl+KP3zmBLSXt9hBcfOEh7w+ohs2oomA5zyQLRcG0JPJu3yZt2TRQu28ZU9zCSmdpocddCJm8xk8iVELdSisvOAD82T/KWdY6U3LyxfzXkVbVlvGIHTYs3TcAMcjR3kAfVgVWJG1icoVeCqaq/toBcwSFfRc44mfsZkmaputhWZAAAIABJREFUk13e2cFE7hfWHHc9cOkaLVH//Oy/doSRzJg1nwCkc+bi9xQNBtjb2lSxc3wiW3nVmMgWFURjc4mKr0/Fl1Y5s+nK1971sSmePNDN1x59kNl0hqu3JsmaRY/tgakYPzxzYUtSxYLlkKqBpHIlaiHThO2Z9z0Ly3aIp2sbo1wJ23FIZIrWqcuhlOL71jtclgOL2z51+nnF9Qxd+o6Vw2wae7SdnHQul8W0W0QDTa4wpikXJV6OVKSzJqZLJ+gz0KqEP/ZqO2mgjhilpBDVghzW19eBJZmxcLv0MgJVeOlP/A5Nvh/g0wexZYTJ/NexZXOVkdaHBd/vuoC75iXbtiPJ5Nd+aG0Epu2QyhZXaS5DX9XJsM5f2dq1LlBUCvmqlLl6PUvbPa7K+xRsm8vDY7Q1RBicKle+TCZS/O5P3mFXcwNP7u+mMbx2Qc6l4VHO3RwhmcsTDfh5dP9uHtnXga+GWvBcwcG0nC1LB7fJ+x5FaUux2iOTt+a7YZe/dlkOlBA3QIIMHzgX2K214uBgiLUvHVs5vGuf55YsLou7tDaeMo4uEm+n3sIxuY9zzjUkxRlSEB9PGUcJGx4cjyz6dC/rFm9aDnFHEvS5cFdoaG0InWeN47xun1mUGgbx8YL/YTzW+jL9jlQkMibRCuEThYep3M+ta5y1oAlByF8k7dtVQp3KWjW9jqSSvHqujzM3holnsoT9Po7tbufJnsrhqMf3d9E3OslsZsk2wed28cieXQCc2NPJpZExUrnSicrBtiUjqa7mBoaqdKZPZPPUBQpYTuUV6kwqw0wqw9BUjJcfOkLvrXES2Rx1Ph9P7O+mqW6J0HtHxvmLjz+lYBVXFNPJNKOzCbwug4f2tNe0W04yY2658nKbvO9BpHPWbdVzJ9KFVZduI85k5e1yit8t/Dk5TJq0CE/qR9mr76w6zvetd7gql3oQDjkTxFWKV9xPL277gvE4u0Qrw3ICt3BzQu+hTiveUAs+3f4VJC6lIpkxCfpcFWOHh/QuusQOLsh+JIoHtb3s8EVJWutP/OYLDqZ367OjShAUZ9rhgKumsrqVkLLYsLmWeL93kL/5pHeRLHOmxesXU3hdLh7qLu1heWl4lA/7BkjlC7gNHY9h0NEY5UR3J3t3NCOVwrQdnj+8n0+Hx5hOpPF5XOxrbSLk99I/PsWe1iaePriXM/1DJc6CUFQjedwGOxuiNNeFmEpUbyQ+k8rwJx+cpbBMXjgwOcPPPf0wrZEwAOcGRhaJewGZQoGP+4fpbmmkoc5bs/h3tmBjO3JLD4Rt8r7HIJUisSJcknZyJJ0cLa5IVbXEeqBQJNMmxhqFCJ4qcWUbZzHBOCQniMkE3xIv06DVIZXkU+cG0ypOvQjTSJj+CoU3V+UQz8gHiWghBpxx3nPOMylnceOiW2sjIMqX2Ysk7lXkzSKJp2WOM+an2Mpkh97IcX0fulgiWp/m5XHtyEa+njIkMxaNkdqRd7HPp+uOdffJFuyaenSncybnbtwqm+U6UnF5ZJyHujspWDZZ0yRbMPnRuUtkC0sPD9N2ivHxHc1cG5vkzU/7GI8nMXSNXY31/Befe4JrY1N82HeDZK6AANqiEV44ephH9nTxzpVrqGXLCAW819vPgbZWnjm4l1cvXCGVq/6ALqzQhc9msnzUd5OvP1Y0qMoUKocpM/lCMembMQkHalONq1RRlli3BX+abfK+x5DKWoudX0xl8x/n3qA3P0xGFWgzGngheJzHAwc2NXYibZIr2ITXIO8T+gEuOjdJValwXECaHGedPp7lGN+13mBITSy+FiFYFssGyGMypmZwSYO/st4nTnpx+3l5HWXBV5bNzJdD1wQBr4uUO8Vfmm8xO/8gueBc56oc5OddL6wrnLNeWLYkX7DxbqHqTiAI+AxCPvemPbc3i1rGuqUqNnwuVKl4zJsWPzr7KVdHJ0nn8xi6jmmX//7Xxyf5zKG9/OjcJeKZosuk7UhuTM7wvZPnmUmmKMy/TwGjc3HeudLHiw8c4sO+fswVD45kLs8HV2/yZM9efu3lJk73DXBhcJR4prK75UrElilhGoKBMt06QP18n85M3sbnMXBVCNdtBpm8vSXy3lab3ENYCAcs4E/i73Imd53MvCpjzI7xvcR7jJrrd1BbQDJTWHeLpjotyCuup9ilteLDQx1BXFWe8wVl8p5zoYS4AeKkKy4xfXjYKZo55/QtEvdy3JCja6pC3rcvLBL3AgbVOKdl71ofbcNI5jZepGRoGkGfi+aIj46WII11vjtO3I4ja6pUSs9/Dy2Ryt2QbEdyun+IZC6PVFQkbigqOM7eGF4k7uUYm40vEvdyTMQTZPJmxYbEAJbjYNkO2ZxFOmsS9nkxVoSjXFXCE7OZzOJs/skD3UQDpZYLzeEgTx1YiufXssrZsmWZWGAj2J5530MoFlJIPshe5kpumMuF4bJ9MqrAyexV/laV2WklJLPmhi+6PXo7e/R2CsrCQOe71uvckKNl+7VrTfQ6AxVGAB9uspQuRQ/rXYS1AHmncsw9Rx5TWatKAqfkXMXtvXKAl6LHUZa26MGy1WSdYxftAVYrndeEwOPS8bp1fB7jjncRr4R0rnaJSqXU4oP/mYP7GJmJMxJb+g12RMLYan05mh3RMHaV5OJqp+t1GXgMo2JLtHSuwMjMLO9c6WNu2Yzb6zKoDwRoioQIuF18eK38Os3mTQanZ+lqbqAtGuFvP/sop64NksrniQZ8PNHTvWg9azkOsZk0LleUQI3aq2Xy9qavl23yvkcglSKTs/iTxLu8m/l01QvZYv1EbNoOmS0krRbi30/rDzIjEySWzZb3ax0c0/fxrn2+4nu9eHhYP8ComkFD0KW1cVDs4qR9GaE0BAK14pM6SH5sneIb7merygG9wl3xTp+Qs/zL+F/wXzW8QqNevOFsW2I5En/ATSFv4TgKKdWGLEQz+SJ5a0Kg68U2aG6XjtvQcbu0mqoQaoVatsVbHjv3e9z83ecf52z/EDPpDBG/n0f37eI7r7635jiNoSDPHd6PxzD46NpAmV9JQzDAXCZb9tsEPG4+vjlYkbgB+sYnuDk1XRaLz1s2u5ob+MLxQ5y9WT4RguJlFEul6WpuWDzHL50oz5W823udT26OMJvJEvH7eGRfJ9988sEtSztzBbuiqmk92BJ59/T0fB34mb6+vl/cyjjbKN5sE2acM9lrqxK3QHDQ07nKHktQKOI18rPo1Fv4FfFFPnauklMF2rQmHtD3MC5jZKicJJolyRnnCj1aJw/pBxiSE/wb+y8X9/fhIUf5+V1Rg5x1WnnEOFhx3AP6Lkbtyl1ThqwpfpI+y9+qK65MFlqYRYIe1IoiJCkVzgKRq9LnQbETmkDTQNMELVEfPs/903onb9aGvBWq7OHv0nUe7ynVzO+IhEvix8vREAzwUHcHj+zdjcdlYDmSh7p2cfbm0KJrYMTv44n9e3j14uWykEu2YDI4tXqosJpUcDKepGA59LS1EPR6SOdLr7eA182B9tVb810cGuXty9cWjdni2RyvXeijzu/l88c3l39aPG9b4ki5KdXRpsm7p6fn/wFeAipPu7axIaSyJlfyw4sNDCpBQ+OpwCEe8Hata8xk2qxpY9mQFuB57UTJtkE1vqjRroQcJudlP+dlf4XXCuhoOBXePyIneYQieReUyWm7l4TKUKcFeUQ7yKAY54YqD+MAjORmoG71zyKEQNcF67VwTufs+4a8Tcthoz2W0/kCQ1OztDdEiASW9Me5wvpalz1/tIcbkzNls2mApw52c6K7qOt2pCKVMXmoaxf7WprpG5/EZegcam/j+sRkxVh5zrKqkvNaSGRzzKVyNNb5eWTPLt65fK3kagt41jb9unJrvOJ3cHFobMvkDWBaEp/nDpI38CHwA+DbWxhjGxR9FExL0ulqwoVRNSyy02jgFyLPrW9My6nataaWaBQRBKvHK1dDJeIGFhOkCZnhu9brTKr5Ig0JV8UgLaKh6kF1qWPZTs1UAVBc3m5Vl3unULAc1vtUUkrx5ycvcuraIPFMnqDXzfHunfzSZ06gadq6vW4aQ0F+4wvP8gdvnSSWSqMAj65zdHc7D3UVV4qK4iRlISwS8vt4eM/uxTH8q8SR6/w+YlXK5FdDLJ3hL89e4OuPPsRnDu3jyq1xJpbpwacSKf785Dn+zrOPVx3DqlJib6140EzFU9yYjLG3tbGk+Gct5E0H3yYUTWu+o6en5+8B/+2Kzb/S19f33Z6enufWe6Bo1I9Rw5uplmhqqpxBv1OYmssSVRClmwcLu/k4VT5LBQi4vUSjazcgkAomYxnC4cqlycCqr20ED6t9nItfpd+qPAteC0YFy1cPLh4NHyDs9vJ68tQScc9jQs3i1z1U4n0BPBk6jNJ1IlF/id5lPd/davD6PURr9L3dTqjZLKmsua7P+8Yn13jt/FUWJpbpvMl7vTdpa6zjm88cI+8o3OsklnDYyz/9uZe4PjbNxFyC/e0ttEbDi6+nsxYer4tqEd5D/jbODQwxOhsv2d5eH+HpQ/v48blPq3qlrIZbs3MMzEwTz/uZSpYX8tyYmOG1T3t55bEHK1bt7tnRUGaeBbBvZzPRqB9HSr7zow843TdEtmAR8Hp48uBufvXlJ1a1DliAz2PQ1LTxXppr/ip9fX2/B/zehkdegbm59eku7zSamkJMT1evzLrdUEoxOp1ZXJb97dALxPJpBqyJsn07teZ1fY/x9OqywHDYS7IGrbCkUuRMm/12N1ksMiJLUqRRG8jhdIk26rQAfc4wKbI0iQgP6wdoyTeSzOcZLcQqvs+2JR2ihRFVWg16VNtDm9lCbDZDIW8S8hVnc9Gof8vXYCadxy4EtjTGncBELEMg6F3X5z11ZYhKUZFz12/x3KG9zMXLJX1roTUUpjVUJO2F60wqxVxqbcuHiN/P2Gx8cVHlNnQe7t5NczDMNx59mAvDI9wYnySxSjFOJYzFEqQyhYqfVQHv995keGqOX3rmUbwr/FZawmHcRqluvT7o57NH9jE3l+Wvzlzm7YtLE65MvsBrn/QR8fl48VjPmueW1ASuVdau1SaX22qTu4yCVRpTdAuDf9D0df7t7GtczA9iYWOgc9i7iy+GH11zPEfKmiWrqsF2JNmCw7Q9yxvGaaa0GZSAkAzQ43QxI+aY0eKVO+MoQICuNJpFlCgh6kWIZ9xfwcSiTgRLqki9wlMxPOLXvLxiPMX7zkUmVbFC84jWxUFjKR+QzdsEfa6alTSblrwvQicb8e12qgTHHSkxa9Ar1ZGST4dHSaTzdDU34fdUV1YMz8S4MjpW8nObtsPFoVt0NjYQ9Hp4av9entq/l9HZOSbjSSYTSfony2fFKxH1++hsauT0jQFyVVQrwzNzfHjtJp89skS4Silev9hXFou35qWoAH1jle0krtyaWBd5O1KhlNqwcmWbvO8ycoXymKIudP5ewxe4WZhgwJxgl7uZvZ719QTM5G9P5xsocmg2Z5Gbfzi8Z5xjUltSAaS0DENijG+YLxATCU4bnzIrEoskLhQcdPawW7ZxTRtiUB9lnBjY8LHo46vGM9SvyLof0boYkGMleQADnaP6Hryahxe0R6qer5SKXMGpaV/CbMG+LW2yagWl1IaS1Ht3NHJxaKxse3dLA9Ya8e7r41NcGBylYFm0RsI8dWBPyaz1VizOX5y5wOR8jNl//SYPde3meFdltdT1iamKM+OR2CxSSrRl10Z7fZT2+ihvXr665mesD/iJBorhjaMd7ZwbGMKu8tBabkULRcvasRVhHIBUvsBHfYN87bEjVFtqbuQ+tB2Fy7iD5N3X1/c28PZWxvhpx2pJxW5PK92e1WVMy6FQ5As2Y840p5yiOiMs/DysH6BTX984Sik+dq5wRQ5RUCbNop5njAcIqRCpzFKyKUuOca1crpcTBfq0QR6RR+mydhInyTVtECkU9bKOAf0WbxlnyIl8ycx8RsV52znHL+qfLxnvkN7FR/alIskv+6R5tT5P5Gzeqil55+5x8t6ouujFYz2MzMxxfmAUy5HoQnBgZwtffewoqWz1+oBzN4f58fneRSOna+NTDM3M8q1nH1vswv7qhd5F4gbImhZnbgzQ1dJIxF8ej5+rkpC0pSRv2RUTmjsidVweqZ5v0YVAAX92+hyCYuHOjmgdM8kUOav83ltpUasJDSFEiafKIuY37W1rpG+sfPbf3drAO5f6QcDj+3dX9DtfgCMlrg0WvG/PvO8iLNvBrsHSdAG5gsMta5o/td5a6ryuiiZS3+A5dq2DwD+0P+Ut59xi8cyEmmXcnOGr5udwqaULey2KSJGhV7+BjU2nbENTgjeMk2S06jHUUTlNQZp4tKWbtF/eYpLShKWN5LTTywP6nqqFPAuwbFm1VHszKJgOUql1JaLuBjbafEDXNP7Lzz9J//g0/eMzdDRGONTRihCCuKz8gFRK8fGN4TIHvqHpWf7DO6dBFKtOR2bKK2ELtk3f6ASP7Sv3Vg/7fYzHKzdnyFsmc5kMH98cJJZM43YZ7N/RwsPduxmajnF9ojx0YWgCXdMXqy4VkLNsRmJzZeXzUDznY7t3MhqLMzgdoyUSpru5gZ0NUYZnSq/BiN/Hg7t3olB86cQhJuMpLg6OYdoOHsOgsynKh1cHiKWKx371k6t888ljHO+u7MJpb6JF3TZ530UUamz7ms1bnHGuLBH3PNLk+Ni5uiZ5K6X4VN4sq3qcJs5FcY0T6vDitgA+WlUjt0TpTeNVbnzKy5+7XyMrikmli+pa8cU1+K6gTL5j/oAOrYWXjEcJaD5G5CSywqNiWsVJqgwRsbZSaKHacNKa4630BWadFFE9xPOBB2h116/5/uVQqqijrkUbq9uBzYbM9u5oYu+OphVjVR7MtJ2qs+SB6coJ5uW4OTXNie5dizP0BXQ0ROkbK0/UA7zbe41YJkN23hY2Y5qc6h8gmcvz0oOH2dPSxIXhEWLJNAhBUyhAUyjE+eFyZ0ugYthEKsWPz/cynUxjOQ6aEHS3NPLiAwf4yYVeRmPFRGpTOMhnj/TgdblQSmHoOn//808yOBVjYHKW3c31/P7rpxaJG2A6meH7Jy9yZNcOXBVknNW+69Vwb16BPyXYiinNSiwkUFYS9wISqtwEqmwMbNKqskIhI8pnzE9ZD/GW6xRTYhYEBKWfY84BruoDi8QNrEnaC1ACkmS4LG+Ss3L8kucLBEVluVsAL/4K9rELmJSznLGvkCJDxArxXOIQfxh7nWlnydDqSmGYv1//RXa6G9d3gvMwLYn3Ho2c1DLfUW2sorWtl2yFgpz1YCaV5u3ePl44eqhk+/Jmwitxay5ekeD6xid4/vABMoUCM6n0YjHP2FxiUwnX5W3ZpFL0T0zTEAzwq597isGpGAXbZt+O5sWKSDWfgAfY3dzA7uYGPuobLAkXLX2+FJ/cuMWj+3eVvbaZn22bvO8iatnsd0EaGKayXjQiqutIJ51Zrsoh3BhERJBchSrPXIUS+Hrq+Ib1IoNilJzIs1fuIk+BD4xPNvkpljCkJhlxJjmu7+e8c41JVboE3693VDWvuuVM8T3r7ZIH2eVbN8mtiJPPOEneTH/Ct+pf3NC51fKhe69i5eprOTQhONrZzvSlvg15xCzHSGwW23FKZt/VVCBQfWYqpeLSyCgXhm6VFM0oYDaTxtC0qsnJ9Z/rHEIIulrW95CvNLNefK2GtS7b5H2XoJRalBrVAtZ8zOwx4xCD5hiJZcSlIQhSeQb7pnWWM04v5ryaw4+nYuHMgH6LS+o6R+S+ku0CQZfauTh1kEgM9A2ZZ1WCgySmEnSIFr7heo637U8YlzHcwmCP1s5njRNV33va6S1bgawk7gXMONVne9VQqOHvdq9CIBCi+uz7mUN78bgNekfGyVs2gsrNhH1uV8WSect2cKQsIe/6QIAbVPasWQ2xVJpkrnxl6EhFR32EiXgca0UiVxOUKVt0TVRM+G60ccbx7nZ2NkS4FStVqXQ0RHhwd2XV2GYyKNvkfZdQC7vSBSjU4qyjRatnv9bJGXll8XWJ4pzso8vZwT69Y3H76LwqxV5GtFkKeHGXkbcS0K8Nl5F3tfPZKvzKy16K59qoRfim+/l1v3dOrb/oKqxtvOrStiVSqjvSDWejqGUedaXKwnaKmu2caXKko51H9+7m0b27gaIx1B+8+SGjy5oZaEKwv62ZT4dGKxClxmsXe6kPBTnR1YnH5eJ4VyfDsVkmE5UfqJoQZTN9t65zsL2N6+OTZY0aAA53tPPc4QNcGB5hIp5ASUXQ6+V4907m0ll6b42TKZg0hoO01IU50z9Qdq4LjoPVzmkldE3jF545znc/OM/wdHHFuKspys8+fbxE7rgcm3En3Cbvu4SNqgJWHWvFg2BclSeNLGwuOwMl5N0nh0qIewEFZVacCuTE2lVtV7Sb2GL1sIIhdWxtaR+XMrCxF+WyhtJpd1qIiTRBY+NNWoPCVzGIuHJFERReng5srlWa5Ug82r1n96DX8IGyfKTRWJwfLtNsv9d7gycPdPPMwb1AMVTwi08/ytu917h6a5ysaeNIycBkjKZwqCwGnDVNBqZnGJieYWx2jp62FvrGil14qmFnfYSJRHJRPeTSNR7d282OaB0djQ3cWFGs01oXZk9rM5oQPHtwqVhmee/TZw/vQyqFrmkopXDrOucHR0jlC/jcLva3tfD8kcqFNkJQdcq8r62Zf/rNF7k+Nj3/d9OqCqXN/G7b5H2XYNfQ7c9aITOyqJxIMldsd1E5ZqxVcfqLqHCFvUtRqfXZStSrOrqsncxqCRwkEkmWHDYSHUFG5LhuDDGgbrG7sIOvuZ7Bp63fU+QhvYdhOUV+md1sWPPzOd9xbjpjzNopokaIzwSOcMDbscpI1eE4iipf311FLas/XS4dZz6X8urFKys02ybv9V6np62F5rqi4ifo8xD2eUnll0JUyVye5Bql7OPxRFWJ4HLs29HK5x84Qu/oGI6U7G9rxbIdXrt4mUw+j9flwnQcBEUp34sPHq5ImMu/IyEE+vw+QgheePAATx7oZiQ2R3NdqKyzTsn3Y+irVu9qQtDT3rzm54Jt8r6vsJES5rVgr9Axt4qGsgQfQJtWmnB5SN/POecqSUoVJp1yBzlRYGJZ9WRI+jnurG1/uU928qnqoyCqKxHSIktUhWlwIrzlOkVOLEuQLsve28KhX93ix/Ypvu5+ds1jL56D3sFXeZpPnGukVIY6EeL58DG69FZe9B5f9ziroVpZ+d2GpomahU7chka+AKlcntFYeZVhwXb4dHiUzx1dui5uTGw8Zr0e7GpsYF9rM6duDDAyM4cjHSYTSaYSqYpNGmLpDCev3+QLD5aurAy9tHnGZDzJ4HSM9voIOxuiQNHdsKetZc1zchm1e1Bu5qG7Td53CbW8+VdKop41HmLKmisJn4QJ4ChJThYIU5zFBjQfL7ue4D37AuNqBjdudspmPmM/go7ORa2POS2JT3k54uyljrU11RHCHLcP8olxlYKonCTManledX1AWIZKiRsqLkOH5SSOkuhCI6vyzMkUzVoU1yrNhvfrnezXl8qww24vZg0tcmvpk15r1Gr27Z4np1PXB6r6aa9sIrBVZcdyBDxudkQjNIfDHNvdwVuXr3JldHzx9bk1mgwPTE4zGU/QElkyd1+wXpVK8cPTF+gdGcd0HHQBe3e08LNPPlSmP8+ZJkIIvK7SpZa7RuQtxMaTorBN3ncNtbz5V8bP67QAv+z+Eh/bVzg1r7xIkuFd5zy9ziC/bL+Eb159sl/vZJ/WwZxK4REuCimxWBRzQh4GCbMiQV4UCKvgukyejstDdJud9GtD9GkDJLR0GSlLoYhr61N6SCSOcvhr60OuyWGyFIgS4oTRwxPG0XWNAdS0mrWWK6daw9BLv2zLdjBth8AGxemGoXHu5hAfXr1Z8fWg17Po1b2A9vpylcVmsbelmc8cKsabc6bJwBrddFbClpKxufgieWtCLPaLPHntJucHlwp4HFU0mPruB2f5pc8UDeCmEkl+cv4Ko7NxNCHobKrniw8dXuxpWauZ92YfttvkfZcga0jelVQrhtApYJVJ5maI80bmHF8WSw2MhRDUizAj9jRntT4kimZZz5SYZVAfJSvyKBSNMspjzgN0qh1VzyVFmo/1y8xocQrKJKVlNqeDWoZ20cx7zgXOy+uL2+ZI8bb9CQ0iwv75JGxOFUjKNA1aBEPUpoqtGqp1Mr8X4JknKMt2+KP3znF5ZJy8adPRGOFLDx/i4M71+dwIBFdGJyt+Vreh89KxQ4T9pbmIzx7pYTqRYmAqtiXNUVMoxI76KJ8MDNEaqWN4OrbYMm290ISgqS7MbDqN7Uj2tjUuXoqDU5UrQfsnpklm8wS8br5/6kKJ/PHKrQlMy+Fbzz2GrolNtS6rBM92A+L7C7WUCVbDyiYGC5iwY2XJtjP2Fd60z2IaxRvk8rLY8wJm9DleEx/wZet5WiiXTw2LCV5zfYC5Srx7LbiVqyh9FDYoaFENfNb9MD9w3i7b18bhijPIXq2dv7E+ok8OkyFPPWEeNg7wmHG4/AC1wj1M3m6XjgX8p/fO8sGVpY7p18amib15hn/yzRfLSLcaLLtyqKk9GuGBXe1l271uF9967nGu3Jrgg6v93JpdOxG5HPWBAN0tjUzFk7x64dKmi4AAmsMhTl2/yWQ8gaMUbfV1vHD0AHtam6qqvaRSnBsYpj4YqKhbH5qOMRFP0NVSXT64UXjc2+R9X6FWt/5qs0kvlZfJXlHqqWwpm1N2b6kapcps2dRsfuh+gwNON086xzDmL6Gz2iVOG5c2Nstesa9LGnzZfhav8jKo3SKoAnSrnUQ8XmxVOeZq4/C2fY5z8tritlmSvGWfo16ES6SRWyGC+wket046Y9I7Um7WFEtneftSP195dH0SyV3N9QxMlU8C2uqrNwkVQnCoYwet0Tpsu2unAAAgAElEQVT+wzsniaWXYtOVimPCPi9N4RAdjQ3oQO/o+LrUJwC7GxvwuV0kcjksx0FJkEpiOsWE5vJDjc0m+NHZS/zaS59hV1M9NyYrh2GUUmTylXvJ2lKSzBYIeGtHnR7XdtjkvoNUko9z15my4+x2tXDYu2tTYv1qeEDfS58cJs9S4lAgOOrtZrm8+5acYo71Vxo6QnLZ6KdfG6ZehQkoP/368JbDI5Zmo6FTR5AHZamypU1rZFqWx1J3aS2cd66Xbbew6XUGS8j7pwWaEEV74CreI9W2V8IrDx/m5kSM4WUOgbsa63nm0N4131sf9PPzTz/MB1dvMpvO4Pe4aQgFGZuNkytYeN0udjU2cLRzJ4lslp9cuFyxTVk1NAQDfPnEg4v3TCDgYTae4bsfni7rEr+AWDrDhcERHt67i7cvXy8v+jF0Hti1E5eu8W5vf5mSpSEU4MDO5pqVuWua2PRY2+R9l5B2cvyLmb/ihlnMnmsIjnq7+NX6l9ArxGurwVI2UsmK1qi79R18QT3OGecKcypFQPg4onXxtO8oM8k0CoUHFxftG5v6DAXNZJx1JJEWQjCqWIDTKKNMGOXv8yo3QVWuqxVC8LxxglkryYgqFmIY6BzUdnFCP8DHdmVDfmeF5vxetXG9HWiJBtjZUMf18dLvWReCgx1ry+AWEPJ7+YdffZ5XP7nGbDpLYzjA8a6ONeO9BcvG0DWa68J8/bFjZAom3/3gYz64WrzWDE2jp72Vo7t2IhB8eO3GhogbihLG6xOTTM4l8XtdHNvTyaWRURIVSuWXw7QdTvYNVFyJ6Zrg1Qu9BL1ejna28cngyGJRkM/t4ukDe6gL1K6PqW+TIRPYJu+7hh/EP1okbiiWsF/I3+T11HleClf37VjAtfwtfpz6mFE7hiEN9ug7+bzxSBnxHzX2cETvxsbBQCepsvy7xE8YMMeRKCIEmaBybLwmUNDqNDKlzyKFxBYOE2IGn/SQ00pnR51OG74V7WkXZFQh/HzL/TK9zgCzKsUurXXR4naH1lBxVt6hrZ+kAK7mR7hhjtNohHnEt39Vr/BarpBuB4J+N188cZh/9/YZ5ubDFpoQPN6zmyOd1RPOleDzuHjm8B4K5toFWDcnZ3ivt5+JeAKPy2BvazNfOH6YNy5eYWh66TqzpeTyyFjRP7y9vWpJ/GowHYefXLi8+PfpG0M0BFfvMRrwujna2cYfvn2y4us50+bqaDHcVOf38oXjh5lNZRBCcLyrg5ZICO8WCHcl/FsIv2yT913CkFm5716lxsMrkbSz/Pv4m8SWmSp97FxBIfmi68my/YUQuDBQSvEX1rsMqqVj5Ki8vFweLBQIlNhEvFjCE/Yx/v/2zjRIjvO877/37Wt67tkTx+LYBRaNBUBcBEQABEFKJCVK1mlFVuIjuqwqVeKUI1VSZbnsL6mk8iWJnZTKzlFxRXHsqGIpkhXJukyRIiGCF0QSBLBocHFjASz2nr1mZ6a782EWs8fM7A5mZ/bs3yds72zP25iep9/3eZ/n/7+gvocrZmwQCZhkki3ORoZEEhWFFncDx50DBadQpMxnY6SQ7FN3FLzmA+qj9GeSdHu5BhEFyW65jUeV2W3NpQKu67n8j8Gf8fbEFbJTnaUvjZ7ny3XPEVeLqzGu9Fl8QFc50LaJr9c/w0sXrpBKp+lo2cC+bRsrevCETW3B4D2amuRvX3+HofHczDfnnHMjZ7JdonzwZt8gx9pb51XiUxVZlpxEdirPrQhRtEImqGs8uWcXZy5fo2+kuHTyTIbHU3Tdu89nTxzJHwuZ1WurlVIQWITLkx+8lwldFv+v11j4qf7y+LuzAvcDupzbZFWnaJkcwG23l5vewmatwKz8dcKNEnGD3JI9s4PwAmhCIUqIpCz8orgCxsQ4n818GG2e21ArowY2IkN8Xv8I7zpXGfJG2CqbaVUK1dtK1eW+NHaeNydm582vZe7x/ZFX+ceJZ4r+jaKs7OANEAqoZLNm2ZuT86GrCoamzCtj/EbX9XzgnknXvV7MIhZmAOqUzVhbcwNnr96c9TtNVTjaup2Olo1cvH2Ht67fJDXl3jOVhStKXTjE4NhYXoLC0FQ6NjXzzP4OTEPjGz/6xYLX+4CBGYYKiiIxjerNuk1DWdQkwA/ey8TB0HbeS802flVROGQWziznMl7CnmqSTN5tvhgjjOEW0SxZiAExzLHsAY5mH+EX2hv0isGyNiezOGiehuqpZEVhydmAHOYV5S2edEqbCKvzNEIMuMP0ekNsFc2YMsABdf5NtFLB+8pkoQEvlF4dQXUFoGpFKKAyPFqe12c5xMI6/cOpkg1mqSKekLnjGTpaNnB3TumdKgW7p2rOnzu0l8lMhq57vaQyWRoiYY7tauVw2xayjkdTfBeHd2yl8/ZdDFXjpc7LjE0Wv7atjXV85NF9vHf3PrqqcKRtG5Gp0sjR1CTjkyVWm0UIB3JpPCEgEdbLalIrl1BgcbN4P3gvE59sPEZvapS3J7oYcsdpVGKcCHVwOLiw5Gq7sYkXx84V1Hg3iUTJ8kCAnbKFGGGGme2qo6ESIsAQJdx2BKSYZBubOJk5zHf15xe+QKDOS7CZJsKuyZBSfDOqW96nlJbVzI64mWS9LN/LvMwV9zZpskQIckjZxZPa/LolpYK3WqLNXptn47haDRq1RFMVAoZCarI65hGKlMTCBgPJ4kJTrY31vHb5WsGMWFUk2xrrSWWy2N09jKfTxIMmh9u2sndLLv+uqwqfOfEoyfEJkhMpNsRj+c7DB4uvgB6mKZb7flzv7aOzuzDFqAhBR8sG2pobaCtinpCveClSw114vbk8N0A0qFfVSEFTZb5Vv1L84L1M6IrkN+Kn+Fj0GIPZERq0GPo8Wh0zORBo44jZzpsTl/NflAhBTqiPzJvP1IXGCXUfL2bfyue6dVROqgd4n7KH684dfpB9hVFmL32jbog2L3cTv6t2lZ51z2jsUT2FTW4DY4wXbEzOZL6VQMBQir7V89mzdLrX8z+PMM4vnXM0yQQdyvaS5yuVgjls7uRXE10FBhIdRukyw9WQNoFc0ElNzl998TAYmkLI1BibKCw3tDY3s3/bZs7d6J4VwEdTab595iyP797JP3nuFP0jY2xMxIq6qUeDJhEzwBn7KvadHtJZhw2JGO/f155vS4fcTH1kIsXtgelcekBTOb6rjfaNpZX8pBA81r6dH711YdZKQVUUsjP0W4K6znOH9rBv6yZMQyW4yFlywXWGFu+jV1HwtiwrBvwvIArowNds2z6z6NGsIx7MKkypY+oP160lhODziWfZH2ilK30HQ2h0ZHYQncfq7AFH1A72RrfxyvBFXDz2yVY2Kg2cz17lbTf3MJDIfFANegEedfbl89LDFJ9BS09yMnOYTuUqA3KYrHB4V3mPa7K7pEAV5Dooi19j7stYjBvu3YJjDi6XnZslg7eqyJIPtkfM7Xw8+hgvj13gvjNERJocCLTx0eixkuMuJxe/EjANFV2TpKtodh0JamSyboEdnBCCTz12kO1N9fzw7PlZIlVZ1+PNKzc4unMb2+cxNwB4/l2b051d+QfAncFheoaG+eIHHs9/b+Ihk9995nGu3e/jWk8/0WCAY3tacdILb6wfbN1CXSTI29e7SWeybK6Ls3fLRs5evcn4ZJrNdXH2b2tBSoGiSGLh6hqWKoqoSpNPpWf4GvC8bdt/almWBfxv4PCiR7OO0FQ5r83UQggheDTYzqNTaZb+ZKpsb8VmtY6ntekd9EvZ6/ww+8u8FRrkZs47s1t5zN1PkOkZj1EiLbPBraeBBIMyifPAjEHk5F8p0moPuY7KY9mDRc8XDGglldaKuckDOPP0reqaAvNULDwdOcSp8CP0ZIaoU8ME59EPV1W5Il10ShEL6fQOLWykUS4CQbxE/lsIgUdxdcGxyTSXuu9xdMp9pxgZx+H8rTsFn2T3wDBvXrlByNCRUrB78wYUKWlrbqStOed6HwoYJNPlXefWhnq2Nsx+iMw1XahFnhtyq6FqlJpWGrz/BPI1ZioUcaf1mRcxlc8tp3a2HDRVVmyM+47bNStwQ05L25UeQdckS5YUaYIEaHe3clfex5lZdeLlGmLOSbvoxmQpWr0WIkW8NXVVwdRL35otopFer7D0rE2Wrl/WNYXMAuVmmlDLcpI3qqjjvBQEAxq6lq7q7FuRkrqowUBysiCAN0bDRf0gFSFoiM4vKzw+mWZkvHg4efHC5bwfZnMswnOH9hbNa1cDIaAuGqhqnhtyio/hYHVSMAsGb8uyvgR8dc7hL9i2/YZlWRvIpU/++ULnSSSCqFX+j6gWjY0L61TXAqGpDI+Wv/M9H6FIgPsDC9euPiAanZ5ZTgxMUiz17BoZXtfO8Z57k3EmSBDlkNzNkxzltPuraS0UAT3KAPcpNICAKe/BIrPibqWHO1oP7XJaVlQIQX3UZJ6yXz7hnGQkOc7VzB1cPAJoHAy080SkeM5fCEHQUJFVqtGtj5nEI8bCL1xmZt7XkZhJ9/0SG9KLIJEI0Ts0gTPjwdhqNBANmvnmoAfs2NTI/h2b5p11hsI6DbEw9wYLS2FnGhn3DI/ws3OdfO1TT8/aPJ55X1eKEILGhIleg3i1oT5UtVpxUalMpmVZjwDfAv6Fbds/Wuj1vb0jK1IVqLExQm/vw7XlVovRiQz9w9VbtJSbOolGAyRnVAx8L/0S77qFLfKbaODOnPZ3zVM5mTnMy9rZBb0qH9DgxkkyRloWbnLpnsqzmcfZ6m1ECIiFDFRFctfp44rXTYwwe5XWgm5Hz/O44nbT5w3RJjfTJBMl3980VFq3JBgcnF+8v1ya68y8B+JKpdh9PZBMMTJeueJjd/8QL5zvYngsRWM0xLOHLBKhII7rMjgySSbrksk6fPPFV7nVP/tB3lIX5zefOEoosPBD79XL1/j7c50LrpQA/tHJI+zenCs3nHtfV4IiBXVRo8CQoRqYhkJT4uENrxsbI0WfdpVuWO4B/gb4rG3b71RyDp/KdXxLEQyoFaVOjqv7uJ2+z+CMzchGESfjFaZAMiJLl3Kz7MANuTrxUnnqtMjSqVxlu7OJaEhHkYK/y7zCOedKvvrjdeciv649RUJOzySFEOxUWthJy4LvX00FOCEoWr64GoiHDcZT2YqMQK7e6+O//vQMAzNm0xdv9/D7Hz1FIhykPhZgaDTNK/aVgsANgMiV6ZXDsV2txIIm52/eIe1kkULkW9ZriaEpxCP6vLIIlSIEJCLV00SBynPe/xYIAP8xt1/JsG3bn6jaqNYJmipRVVk1h5eArhTNNS5Es6zjt/UP8ZpzkRFvjLiIcEzZy1+mf1z09RoaUTdMUpa3DHeFN68G7qSYJBY2UKTgfPYKZx171u/veH38PHuWT+tPzTqe9jKMehNERahkV6mmyqrmLQ19cV1xy4mUgkTUoK+CzcufvXN5VuCGnMTqT9+2+ezJQwgEibBBsoQo1ODoONfv9/Fa1w0GRsYIBwwObm9h//biD9+Olg1504iM4/DnP3mJ/jkt7c3x6LxlgeUiRG5fIBLUqr45+YBY2Kiq5yVUGLz9QF09goZKMludLjiBwAyojFawNI7LCB+Sj806tkHW0+cWNjNs8BpocZt5SbxZtgys6RmFfpVTNKqxfMfii9m3ir6m2502tvU8j+ezb3LBucYIY9QR5aC6ixNFLNGqXZ8bXGRjxXITCmikTIfRInXa89E7XDy1eH/O8aZY8XLVgK7xf197J+8k3zM8ws3+QTzgQIkA/gApBCHDmBW8dU3hmUesRTdLGbpCNKjVJE3yANNQiFWhrnsuq2vbfA1S7WAQNNSquYc/qR6kWdTNOtYuttCsR9EVlY1uY9nnspxWmt36ghl4HdG8D+WgO8IwxTddvRk7qmec85xxzpNkDA/oJ8kvsm9xMXtt1t8oUlRViwJYdFfcSiARNdAf0gAgGjSLHo/NceR5Ys8O4nOOKVIQ1LV84H5AJuvw9rXbLMTLF7u42Tdb+TKdcegeqNwrU5GCRMSgLhKoaeBWFEF9rLrpkges/jtxlWNUmOooxqSb4fVxmwkyWF4ruljcrLNOxviC/mu85dgMuiMEMbns3eS77i9AgkkAHW2WA0/EDSFgWozKg63uRo55+zHQuSd6uCC7yOISFSGOKXuITeWy73p9JTsuo2Ja6vM951bB77M4dLrX2UNr/ljQrO4yWNdk1ZzZlxMpBA0xk7v9Y2X3GZzY3UrX3b5ZPpLxoMmT+6b1ZC7euse3Tv+KoalSP1VKmuNhTu7ZyblrxfVjRlMLp3DmBu4HzJSYLRchcsqA4SrfG6XeqzFm1kxKwQ/eKwDTUB96GTuXdyau8p3h0/RNqQ0mOMfT6hE61O2LOu+wN8pV5w7dXh8pJmdtPE6QIoBGh9zOJBnihDki92Ki8yvXZowJNij1HDB2oMrc7CZKC7tKbDJuEU0ECTA+p21AIHhGmRavypQQQ5l5XFNlVTcqofopmOVEUyUNMZO+4YmyAviRnVsAj9OdV3PVJrEwT+/fxbbG3MrMcV2+/co73BucTqNkXZdUxuFkRyuDo2NFtUjqIvPrb0NpKd8Hew9vdt3gwu27ZF2H+nCYJ/e0kwjPruowNIWAoWLqypJpsSciRsX+lOXgB+8VQDioLSp4ZzyH7yVfyQduyLmr/zx7lnalpaTw0kK4nsv3Mi9z1yvtlpMiQ7Os4wl1thb3UxTvnJyPiAyxT2njdefirOOPyDa2qNPGChtFfdExbRK5hg0hIF7lzjghqlu1shIIBlTqvEDZ5apHdm7lyM6tRX936XYPt4todvePjPHa5Rt88KBF560ebs14TdQMcHxX24Lv29bcQNe93oLjrc0NnL7Uxc/P2Xn97pu9g9wdHOZLT5/ANHSChkJAV5d8xRQP60SC1c9zz2T1rwHXAIamLOoJ/fbEFXqyhV+cAZJcnCHg9LB0utfnDdx5qmjse0oepJF4/mcdlRizN8GeUg/RImbn23eKlvyGZSSoVz2PGTSWPgAsBWFTI1GFhqP5UgOKFESDJh8+sodNdTHiIZP2DQ38s48+wZH2zURDOqah5iUj5nLcauPojq0E9dzKx9Q1Drdt4YTVxrnr3QXGC/eGkly4dZumuEnY1Jf8c4sENWLh2jdxra2pxCqmHKeSUpQqkwMWlfce8cpragkXaXFfCM/zuOTeoN9L0io2slnJBePnnTfoZfpBlCbLK+67bHaaaFdy6ZaQNPmc/hHOOVcY9JJskPXsljnzZkNTFq2TXIxaz6KWk2hIx3E9kmOVVz3t2tzE9qY6rs9xmm+OR3hf+zZeePc9vvvqubyS39DYBH//ts2Xnj0+q5TTw8NxPLKOS8ZxcZ2c8PFnHj/MB0bHud03wJaGBPXhEJPZLCMlcub3k9XvJi2HUEClrgpdnuXgB+8VQiigMjRS2cbl/kArLWoDt7OzZ8mb1XqOx9sZTFb2peyQ2znNudJWaVPMpxpYjFF3nO9kXuSml2u8OI3KHqeVj2mPc9MtbMZwcLGd6/ngDTlLtIPqbO1zIaojtTkXXZM1zV2uBBIRAyGo2LxBCsE/PHmYb53+VT6At9TH+fTxAwgBL7z7XoFZw9krtznR0UNHy3RKTCBQFYGqSOaGwHjYYMeG6U5az9NpjIa50VvYFHT+xj3uDgyzsS5W0fVUQtjUqIsunWyCH7xXCELkBGsq+fIoQvLZ+Cm+PXyaG5mc+8tWrZFPR58goGlEQvDC8DtcdK4xQZpNw/U85u2lSdbNe96YDHNE2c0Z5wJZigtOBTCwZPE8aCl+nj2bD9wAGbK8475Hi9NUspennEdaLGzUZIm8lmfdM4mHDaQUDCYr09tp21DPH3z6GezuHrKOy54tOeW/uwPD3BsqrBPPui6X7/TOCt4PgxCCU3t38FcvncWdM+lJTqT40a86+eIzpWV9q0k0pFcl/fQw+MF7BREN6oyOZyqafe8wNvEvGz9D1+QdPDzajc353fhXM+f5Sfa1fKXI/clBbtHL5/QPE5LF63cvZW/wunOBfi9JhCBhEUB6km768oFcIjms7CIhow811pkNNzO54d6hRTYx4M4WJZII2pXSxgiQkz2dT4mwUmpRtbKSiQZ1VCnLrkKZi5xyspl9TpOoaZCcKHwo1IWL33/l8sSeHbx88WpBugZyMrK1Jtf2bizLA3793JWrACkF0bBe8cxHCsGuwOaC42+MXy7QFulnmNedTt4vC2XYu51efpj9JeP5dMkEQ16SZ9SjvF8c5oJzDRePXcoWdioLa4vMRRFK0am0ROFZ9SgjmTFuePdw8TAxOKS0s1vZVvJ80ZBeszK+eNhYstKylUIwoNKsBOkbTlVFuiEU0Nm/fROnO2c3UW1rTHDcai3xV+WzMR4tGrxDZWqpVIoicw04y9W45QfvFUbE1BgZS5N1qlPB4Xouw27xrsXREhuSbzuXZwTuHB7Q6dzgmLGPLUply9wHbJcb6XFmf9lUFDqUbQRlgN/SP8R19y593jC75BZisrRDUDSk12SDEnJaMcF1NOueiaEpbKwLMpBMMZYqX6O9FL956ghBQ+firR4yWYdtTQk+8dgjVUlzHd+9nXdudDM+OV1uq0gxVZteGwKGQkMssKxepuvzzlzBCCGIRyoTDyqGFJImNU4yXRioG2S8yF9QcoMy5VVHe/xp9VHGvRTvubdIkSZGmEcVi11KLncuhKBV2UQrm0qeI7c5adRUayS+BOVeKxkpBQ1xk8BEhoFkalEVoaoi+QcnHr72vxx2tzTzW6eO8PKlK9zpSxIPBXhs13ZO7d258B8/JLkeAqMmG+MPix+8VyChgMaInqmay85Tof3czQww5k0/ELarGziq7i76+mZRRyc3Co43yDhj3gQa6qJKEBWh8En9FCPuGP1ekk2y4aHOp0hBLGxUXVJ3JqGAuuYrTMolbGoYmsJAMkWqSvdktTnavpUPvm83ff2jNZsN65qkLhqo6X33MPjBe4VSHw08lPbEfBwO7iSqBDkz3sm4O0lbpJmTyj50oTE8li54SBxT93HNvcsNb7qdOYzJoJvkG5PfxkCnVW7kI9oJtAq7NyHXURlh4fbomZiGSjSk1URz+QGKIpasVne1oKmS5rogY6kMgyOTOFVK61WbWgRuKcWSdEw+LBU76TwsvpPOw5McT1e8eTkfiURwlqvM+GSWkfH0rHKrrOdw1rlErzuEhspF9xqjzNZqDqDziLKDp9Ujiwri5aBIQTRkEKhwNjz3muejMW6u+lx3Le9r1/MYHk0zMp6uZnPtonmYz7hcct2S+rLmtqvqpOOzNESDOhOTWVKTtV2qBg0VQ5MMj2eYnMxtTqlC4TF1LwC/yLxdELgBUqR5w+kk6Y3xG/rTJc/f5w5zzukCPPbKNpqV+evLi40vGqqO4/ZChE1t1QfuWiOFmCqP00iOpRmdyKyoIL5YcuYMKrGQXnUD4mri36UrnFz6ZLygCaHaKFJSFzaY0BXGJjJkZpSIpZm/ceiqe4ceZ6BoUD6bvcQL2bNMTJ3jTecST3gHOa7uW3BMuqbk861LgaqIJW+0WM2oSi4HHAvrJMcyjE5kan6f1hIhcg/vaGjp9VAqYeWPcJ2jKpKGGom5F8PUVRpiJg1T9atCQJvcjJznVsmQpYfCOtu0l+GV7Lv5wA0wSYZXs+cZd4tX00gpCAVUGuMB6pdwc0gIaIibSLm+arqrgSIliYjB5oZQRUYPy42mSuIRg82NIeqigVURuMGfea8KTEMlETEYHKl+/rsUmqoQDyt4nk44tR17uL3AW/IBIQK0io0Fx7vc2wxRKBA0ygR/m3mJSTI4uGyWjXwwcJSEGcQ0lJqL5BejIbZyqghWK1IKokGdaFAnk3UYncgylsqsyM1NRQqCAZXQEq7sqo0fvFcJ0ZBOJusu2rThYRFCEDZ1vhh4hveNt/P9kTN0O/3Tv0dwQNlJRBZWjYQJIhFFneO7vO78v+84fYxmR/k9/ePLErjj4dp1aK5XNFUhEVFIRAwm0w6pdJZU2mEy4yxbflzXJAFdxTQUDG3pTBlqhR+8VxF1UYOs4y5Lra0QgkdC29kX3MZr45foTN3EE9ChbWO/toNMdsrAzPPwvJzka0AohLMmyTKkZe3J23SmbrLHzLXBZz2HM2Od3M8O0awmOB7anWurrzKhgLok2svrGUPP6dXHyFWqpCZzQTyddchk3ZrMzBUp0FSJpkoCU++/nBUjtcAP3qsIIQSNcZOewXHSmcVrTlQ6hmOhDo6FOuZ93ZmxTr4zdprxMrsyXTxuZ/rYY25j1Jngz/t/yLXMdJ356xM2X6n7NYJK9QKtaSg1M4f1KY4UuXTFzIoex3XJZF3SWRfXzel5O5439W83P1N/EOIFuT0KKQWKIlGEyHeDanho6trwGl0IP3ivMqQUNCeCyxrAF8LxXJ4ffbvswA2gobLTyLXD/93IG7MCN0BX+g4/Hn2DX4+drMoYA4ZCQ9xc9UvntYAiJYouCSyyByYWNkhPVG4osdqoKHhblhUC/hqoA8aA37Ftu7jOp0/VkVLQlDC5PzixIgN4v5PkTrZ/4RfO4KDZSpuR2/S8nSl+K91Kl2HJVgbmVOCWfuD2WcVUurb4MnDWtu0ngG8Bf1S9IfmUgyIlzYlgxR2HtSQsA0RK6ITPJCQC7DW28anoCT6XeDZ/3Cihc2LIxW8qBgMqjX7g9lkDVDTztm37Ty3LehA1tgKF3lVzSCSCqCu0W6mxMbLcQ6iYpqYIvYMTjIw/3HIxkXh438myz02QQxM7eGno/Kzjm/V69oW3Me5M0hJo4Ln6w+hFAvLjXgeX7tzGYXpVoaHwRMMeEvHKx926NUF9bHHi/6uJ1XxfV8p6uuYFg7dlWV8Cvjrn8Bds237DsqyfA48Azxb+5WyqrTlQLVaytkm5CADHYWhksqwyrFpoQMzl08EnEBnJpclbZNwMW/UmPsJVgvoAAARfSURBVBY5xkZ9ugtzbDjDGIWljwdFOx+NDvPauM1gdoQ6NcKxYAd7vdaKxi0EWDsamRhNrfrPulzWwn39sKzVay71QFq0MJVlWbuBH9q2vWO+1/nCVLUnlc7SN5Ra0EZtKYL3TDzPq2hj0PEcRt0UYWmiVKgiqKqSxliAzZvia+ZzLoe1dF+Xy1q95lLCVBV9IyzL+rplWb8z9eMYsDJFftcZAV1lQ/3Ky4NXWtGhCIWYEqo4cAcDKhvrguirtIPOx2c+Ki0V/Avgm1MpFQX4QvWG5LMYVCWnuzwynmawzDTKWkORgrqo4XdN+qxpKt2w7AGeq/JYfKpIJKhjGioDyRQTNZaUXUmETJW6SMAXmPJZ8/hNOmsYVZE0JXLuJ0Mjk1UzNV6JaGpO2W65nLx9fJYa/05fB4QCGkFDZWQiQ3JsbXWgqaokHq6dg7yPz0rFD97rBCFycp1hU0M3dYaHJ1a1cL6iCGKh3PX4Le4+6xE/eK8zchZWAdKNIcZTOe/KldhiX4qAoRAxtSmjCD9o+6xf/OC9TpFCEDY1wqbGZMZhdDzDWGplehFKOT1WTV37anE+PuWwZO7xPj4+Pj7Vw5/G+Pj4+KxC/ODt4+Pjswrxg7ePj4/PKsQP3j4+Pj6rED94+/j4+KxC/ODt4+Pjswrxg7ePj4/PKmTdNulYliWBPwMOAJPA79q23bW8o6odlmVp5KR8twMG8K9t2/7+sg5qibAsqwk4Czxr2/al5R5PrbEs6+vAxwEd+DPbtv/7Mg+pZkzd198kd187wJfXw2cM63vm/UkgYNv2ceAPgH+/zOOpNb8N9E+ZRn8Y+MYyj2dJmPpy/xdgYrnHshRYlvUUcAJ4HHgS2LKsA6o9HwFU27ZPAP8K+DfLPJ4lYz0H75PAjwFs234VOLK8w6k5fwP88Yyfs8s1kCXm3wH/Gbiz3ANZIj4EvAt8F/h/wA+Wdzg15zKgTq2ko1DEFHWNsp6DdxQYnvGzY1nWmk0j2bY9atv2iGVZEeDbwB8t95hqjWVZnwd6bdv+yXKPZQlpIDcR+QzwFeCvLMtaywpeo+RSJpeA/wb8p2UdzRKynoN3Ephpyyxt217Ts1HLsrYALwB/adv2Xy/3eJaALwLPWpb1InAQ+J+WZW1Y3iHVnH7gJ7Ztp23btoEU0LjMY6olXyV3vbvI7V9907KswDKPaUlYszPNMvgl8DHg/1iWdYzcUnPNYllWM/BT4Pds235+ucezFNi2ferBv6cC+Fds2763fCNaEk4Dv29Z1n8ANgIhcgF9rTLIdKpkANDI+equedZz8P4uuVnZK4Bg7Zso/yGQAP7YsqwHue8P27a9Ljby1gu2bf/AsqxTwOvkVtb/1LbttWxi+ifAX1iW9TK56po/tG17bJnHtCT4krA+Pj4+q5D1nPP28fHxWbX4wdvHx8dnFeIHbx8fH59ViB+8fXx8fFYhfvD28fHxWYX4wdvHx8dnFeIHbx8fH59VyP8Hyjdfiv1jeBMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=GMM(n_components=4,random_state=42)\n",
    "plot_gmm(gmm,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm=GMM(n_components=4,covariance_type='full',random_state=42)\n",
    "plot_gmm(gmm,x_streched)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing the covariance type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**the covariance_type option  controls the degrees of freedom \n",
    "in the shape of each cluster**"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "covariance_type=\"diag\"(default):the size of the cluster along each    \n",
    "                                dimension can be set independently\n",
    "        \n",
    "covariance_type=\"spherical\":all dimensions are equal,similar to k-means\n",
    "    \n",
    "covariance_type=\"full\":each cluster to be modeled as an ellipse with \n",
    "                       arbitrary orientation    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GMM as Density Estimation"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Fundamentally GMM is an algorithm for density estimation.\n",
    "The result of a GMM:a generative probabilistic model describing the distribution of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2201d33ba58>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "x,y=make_moons(200,noise=0.05,random_state=0)\n",
    "plt.scatter(x[:,0],x[:,1],c=y,s=40,cmap='viridis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm2=GMM(n_components=2,covariance_type='full',random_state=0)\n",
    "plot_gmm(gmm2,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gmm16=GMM(n_components=16,covariance_type='full',random_state=0)\n",
    "plot_gmm(gmm16,x,label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The mixture of 16 Gaussians models the overall distribution of the input data**\n",
    "\n",
    "**400 new points drawn from this 16-component GMM fit to our original data**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2201d4c3588>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xnew=gmm16.sample(400,random_state=42)\n",
    "plt.scatter(xnew[:,0],xnew[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How many components?\n",
    "\n"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Means of correcting for over-fitting is to adjust the model likelihoods \n",
    "using some analytic criterion such as the Akaike information criterion (AIC) or the Bayesian information criterion (BIC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'n_components')"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components=np.arange(1,21)\n",
    "models=[GMM(n,covariance_type='full',random_state=0).fit(x) \n",
    "        for n in n_components]\n",
    "plt.plot(n_components,[m.bic(x) for m in models],label='BIC')\n",
    "plt.plot(n_components,[m.aic(x) for m in models],label='AIC')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('n_components')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The optimal number of clusters is the value that minimizes the AIC or BIC**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This choice of number of components measures how well GMM works as a density estimator, \n",
    "not how well it works as a clustering algorithm**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example: GMM for Generating New Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits=load_digits()\n",
    "digits.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_digits(data):\n",
    "    fig,ax=plt.subplots(10,10,figsize=(8,8),\n",
    "                       subplot_kw=dict(xticks=[],yticks=[]))\n",
    "    \n",
    "    fig.subplots_adjust(hspace=0.05,wspace=0.05)\n",
    "    for i,axi in enumerate(ax.flat):\n",
    "        im=axi.imshow(data[i].reshape(8,8),cmap='binary')\n",
    "        im.set_clim(0,16)\n",
    "        \n",
    "plot_digits(digits.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 41)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca=PCA(0.99,whiten=True)\n",
    "data=pca.fit_transform(digits.data)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22021cf0860>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_components=np.arange(50,210,10)\n",
    "models=[GMM(n,covariance_type='full',random_state=0)\n",
    "       for n in n_components]\n",
    "acis=[model.fit(data).aic(data) for model in models]\n",
    "plt.plot(n_components,acis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "gmm=GMM(110,covariance_type='full',random_state=0)\n",
    "gmm.fit(data)\n",
    "print(gmm.converged_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 41)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new=gmm.sample(100,random_state=0)\n",
    "data_new.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "digits_new=pca.inverse_transform(data_new)\n",
    "plot_digits(digits_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
